Solving Systems of Equations in Two Variables by the Addition Method

Vertical lines have an undefined slope because the horizontal change is 0 — you cannot divide a number by 0.

The equation for slope-intercept form is: y=mx+b In this form, m is the slope of the line and the b is the y-intercept.

Writing Systems of Linear Equations from Word Problems

1. Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find.
2. Translate the problem to an equation. Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents.
3. Carry out the plan and solve the problem.

Word Problems involving Linear Equations

1. Read the problem carefully and in its entirety. You have no idea how many times this step is missed.
2. Write a linear equation based on the information given. This involves what we just went over.
3. Solve the equation.
4. Check your answer to see if it makes sense.

1. Write both equations with x– and y-variables on the left side of the equal sign and constants on the right.
2. Write one equation above the other, lining up corresponding variables.
3. Solve the resulting equation for the remaining variable.

1. Step 1: Graph the first equation.
2. Step 2: Graph the second equation on the same coordinate system as the first.
3. Step 3: Find the solution.
4. Step 4: Check the proposed ordered pair solution in BOTH equations.
5. Step 1: Graph the first equation.
6. Step 2: Graph the second equation on the same coordinate system as the first.

There are three types of systems of linear equations in two variables, and three types of solutions.

• An independent system has exactly one solution pair. The point where the two lines intersect is the only solution.
• An inconsistent system has no solution.
• A dependent system has infinitely many solutions.

Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method. Substitute the solution back into one of the original equations and solve for the third variable.

How To: Given a linear system of three equations, solve for three unknowns.

1. Pick any pair of equations and solve for one variable.
2. Pick another pair of equations and solve for the same variable.
3. You have created a system of two equations in two unknowns.