Solving Systems of Linear Equations by
Substituting!
Just Follow The Directions Below in Green and the Example in Brown.
Step1: Write down the two given equations.
Equation 1: x + 2y = 10
Equation 2: 2y - 4x = 20
Step 2: This method is best when used to solve an equation that has a variable by itself. So solve for whichever equation has a lone variable
Equation 1: x +
2y = 10
- 2y -2y
x = -2y + 10
Step
3: Substitute the modified expression into the other equation for that
variable. In the example, the variable in the modified expression
is x, so you should substitute the equivalent of x, which in this case is -2y +
10, for the other x in the second equation. Then solve
for the other variable.
Equation 2: 2y - 4x = 20
2y - 4(-2y + 10) = 20
2y + 8y - 40 = 20
*distribute
10y - 40 = 20
+ 40 +40
10y = 60
y = 6
Step 4: Once you have solved for a variable, substitute the value from Step 3 for its variable in the modified equation from Step 2.
Modified Equation 1: x = -2y + 10
x = -2(6) + 10
x = -12 + 10
x = -2
Step 5: Write down the solution.
Solution (-2 , 6)