Helpful Tips

A General Rule for Solving Equations

• Simplify each side of the equation by removing parentheses and combining like terms.
• Use addition or subtraction to isolate the variable term on one side of the equation.
• Use multiplication or division to solve for the variable.

In mathematics, the order of operations define the priority in which complex equations are solved. The top priority is your parenthesis, then exponents, followed by multiplication and division, and finally addition and subtraction (PEMDAS).

1. Draw a line to separate the two sides of the equation.
2. Do Undo Line – this is another strategy that can help students.
3. Color-coding to help with combining like terms.
4. Making sure to actually say (and make students say), “2 times x equals 5” as opposed to “2x = 5.”

To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself. The inverse operations are: Addition and subtraction. Multiplication and division.

If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax+by = r is called a linear equation in two variables. (The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax+by = r. Let’s look at the equation 2x – 3y = 7.

Both equations are already set equal to a constant. We can add the two equations to eliminate x without needing to multiply by a constant. x+2y=−1−x+y=33y=2. Now that we have eliminated x, we can solve the resulting equation for y.

The steps for solving linear equations are:

1. Simplify both sides of the equation and combine all same-side like terms.
2. Combine opposite-side like terms to obtain the variable term on one side of the equal sign and the constant term on the other.
3. Divide or multiply as needed to isolate the variable.
4. Check the answer.

Steps for Using Linear Combinations (Addition Method)

1. Arrange the equations with like terms in columns.
2. Analyze the coefficients of x or y.
3. Add the equations and solve for the remaining variable.
4. Substitute the value into either equation and solve.
5. Check the solution.

Answer. Step-by-step explanation: Multiplying the top equation by 333 and multiply the bottom equation by 777 and then adding will eliminate the variable ‘x’.