1 Answer. The result of adding the system of equations 2x + y = 4, 3x – y = 6 is 5x = 10.

The Elimination Method

1. Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.
2. Step 2: Subtract the second equation from the first.
3. Step 3: Solve this new equation for y.
4. Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.

The method of solving “by substitution” works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, “substituting” for the chosen variable and solving for the other. Then you back-solve for the first variable.

To solve systems using substitution, follow this procedure:

1. Select one equation and solve it for one of its variables.
2. In the other equation, substitute for the variable just solved.
3. Solve the new equation.
4. Substitute the value found into any equation involving both variables and solve for the other variable.

The first method of solving systems of linear equations is the addition method, in which the two equations are added together to eliminate one of the variables. an equation. Since the left and right sides of any equation are equal to each other, we are indeed adding the same amount to both sides of an equation.

By adding each equation we eliminate the variable Y . The result of adding the system of equations is the expression 5x =10. Feel free to ask for more if it´s necessary or if you did not understand something.

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an “inconsistent” system of equations, and it has no solution.

A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.

The solution to a system of linear equations is the point at which the lines representing the linear equations intersect. Two lines in the x y xy xy -plane can intersect once, never intersect, or completely overlap.

Recall that a linear equation graphs as a line, which indicates that all of the points on the line are solutions to that linear equation. There are an infinite number of solutions. If you have a system of linear equations, the solution for the system is the value that makes all of the equations true.

A set of equations with the same variables. The solution of the system is the ordered pair that is a solution for all of the equations.

A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system.

−4. −2. 5What is the y-value in the solution to this system of linear equations? 4x + 5y = −12.

consistent system

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.

therefore, there is only one solution to the pair of equations.

THE CORRECT ANSWER IS: D. Multiply the second equation by 3. Then subtract the second equation from the first.

The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.

In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Substitution Method

1. Substitution method can be applied in four steps.
2. Step 1: Solve one of the equations for either x = or y = . We will solve second equation for y.
3. Step 2: Substitute the solution from step 1 into the second equation.
4. Step 3: Solve this new equation.

Here’s how it goes:

1. Step 1: Solve one of the equations for one of the variables. Let’s solve the first equation for y:
2. Step 2: Substitute that equation into the other equation, and solve for x.
3. Step 3: Substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

The method of substitution involves three steps:

1. Solve one equation for one of the variables.
2. Substitute (plug-in) this expression into the other equation and solve.
3. Resubstitute the value into the original equation to find the corresponding variable.

Mean substitution is a method in which missing observations for a certain variable are replaced by the average of observed data for that variable in other patients.

Substituting for a Variable If you know the value that the variable is equal to, you can substitute that value in for the variable in the expression! Let’s look at an example. Since we know that x=5, we can directly substitute or replace the x in the expression x+3 with a 5 to solve for y!

The following are common methods:

1. Mean imputation. Simply calculate the mean of the observed values for that variable for all individuals who are non-missing.
2. Substitution.
3. Hot deck imputation.
4. Cold deck imputation.
5. Regression imputation.
6. Stochastic regression imputation.
7. Interpolation and extrapolation.

Regression imputation fits a statistical model on a variable with missing values. Predictions of this regression model are used to substitute the missing values in this variable.

Hot-Deck Imputation:-Works by randomly choosing the missing value from a set of related and similar variables. Cold-Deck Imputation:-A systematically chosen value from an individual who has similar values on other variables. This is similar to Hot Deck in most ways, but removes the random variation.

One way to handle this problem is to get rid of the observations that have missing data….

1. Do Nothing: That’s an easy one.
2. Imputation Using (Mean/Median) Values:
3. Imputation Using (Most Frequent) or (Zero/Constant) Values:
4. Imputation Using k-NN:

Fill-in or impute the missing values. Use the rest of the data to predict the missing values. Simply replacing the missing value of a predictor with the average value of that predictor is one easy method. Using regression on the other predictors is another possibility.

The only true way to distinguish between MNAR and Missing at Random is to measure the missing data. In other words, you need to know the values of the missing data to determine if it is MNAR. It is common practice for a surveyor to follow up with phone calls to the non-respondents and get the key information.

Popular strategies to handle missing values in the dataset

1. Deleting Rows with missing values.
2. Impute missing values for continuous variable.
3. Impute missing values for categorical variable.
4. Other Imputation Methods.
5. Using Algorithms that support missing values.
6. Prediction of missing values.

@shuvayan – Theoretically, 25 to 30% is the maximum missing values are allowed, beyond which we might want to drop the variable from analysis. Practically this varies.At times we get variables with ~50% of missing values but still the customer insist to have it for analyzing.

Statistical guidance articles have stated that bias is likely in analyses with more than 10% missingness and that if more than 40% data are missing in important variables then results should only be considered as hypothesis generating [18], [19].

Missing data (or missing values) is defined as the data value that is not stored for a variable in the observation of interest. The problem of missing data is relatively common in almost all research and can have a significant effect on the conclusions that can be drawn from the data [1].

Therefore, in all events, a single variable imputation (with or without auxiliary variables included as appropriate) is conducted if only the baseline variable is missing. If both the dependent variable and the baseline variable are missing and the missingness is monotone, a monotonic imputation is done.

Due to the fact that ML models perform better with more data, the former is usually preferred. However, you should keep in mind that the imputed data should not affect the distribution of the feature. This is especially the case with features with a high percentage of missing values.

There is various ways to handle missing values of categorical ways.

1. Ignore observations of missing values if we are dealing with large data sets and less number of records has missing values.
2. Ignore variable, if it is not significant.
3. Develop model to predict missing values.
4. Treat missing data as just another category.

The simplest imputation method is replacing missing values with the mean or median values of the dataset at large, or some similar summary statistic. This has the advantage of being the simplest possible approach, and one that doesn’t introduce any undue bias into the dataset.