Page 398 - Algebra 1

The value of x in the solution is -4. The y-value can be found by substituting -4 into either of the original equations.
First Equation
y = 2x - 5
y = 2(-4) - 5 y = -8 - 5
y = -13
Second Equation
y=5x+7 y=5(-4)+7 y=-20+7 y=-13
The solution to the system is (-4, -13).
Using the Distributive Property
Solve the system of equations by substitution. Check your answer. 12x - 6y = 12
Example
2
Hint
You can substitute for x or y. Choose the equation that is already solved for a variable.
x = -2y + 11 SOLUTION
12x -6y = 12 12(-2y + 11) - 6y = 12 -24y + 132 - 6y = 12 -30y + 132 = 12
-30y = -120 y= 4
Write the first equation. Substitute -2y + 11 for x. Distribute.
Combine like terms.
Subtract 132 from both sides. Divide both sides by -30.
The value of y in into either of the
First Equation
12x - 6y = 12 12x-6(4)=12 12x - 24 = 12 12x = 36
the solution is 4. The x-value can be found by substituting 4 original equations.
Second Equation
x=-2y+11 x=-2(4)+11 x=-8+11 x=3
x=3
The solution to the system is (3, 4).
Check To determine whether the ordered pair satisfies both of the original equations, substitute the x-value and y-value into the original equations.
First Equation
12x - 6y = 12 12(3) - 6(4) 12 36 - 24 12
12 = 12 ✓
Second Equation
x=-2y+11 3 -2(4)+11 3 -8+11 3=3 ✓
Lesson 59 383