Nashville Learning Center SAT Tip

SAT Tip: Solving Systems of Equations by Substitution

A system of equations is a set of two or more equations that you deal with at one time. When solving the system, you must consider all of the equations involved and find a solution that satisfies all of the equations.

Step 1: Solve one of the equations for one of the variables either x or y.

-2x + 3y = 8 
3x - y = -5

Step 1: Let's use the 2nd equation 3x - y = -5 and solve for y by subtracting 3x from both sides

            3x - y = -5
           -3x         -3x
           ----------------
                 -y = -5 - 3x

Since our y is negative we will multiply the entire equation by -1 to get rid of the negative sign in front of the y
                -1 (-y = -5 - 3x)
                  y = 5 + 3x

Step 2: Now substitute the value of y that you found in the previous step (y = 5 + 3x) into the first equation -2x + 3y = 8 

-2x + 3(5 + 3x) = 8 
-2x + 15 + 9x = 8

Step 3: Combine like terms -2x + 9x = 7x and 8 - 15 = -7 (you subtract because you are crossing over the equal sign)

7x = -7

Step 4: Solve for x

x = -1

Step 5: Substitute the value of x into one of the original equations and solve for y.
3x - y = -5
3(-1) - y = -5
-3 - y = -5
-y = -2
y = 2

Step 6: Check your answers

x = -1 y = 2

3(-1) - 2 = -5
-3 - 2 = -5
-5 = -5

Your answers are correct (-1,2)

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