Question

Use the system of equations to answer the questions.

5x+4y=3
y=−2x+6
The value of y from the second equation is substituted back into the first equation. What is the resulting equation?



What is the value of x?



What is the value of y?

Answer 1

Answer: x=7 or y=-8

Replace y with -2x+6 in the first equation

5x+4(-2x+6)=3

Then solve for x

First, distribute 4

5x-8x+24=3

Combine like terms

-3x+24=3

Subtract 24 from both sides

-3x=-21

Isolate x by dividing -3 to both sides

x=7



Replace x with 7 in either equation and then solve


y=-2(7)+6

Multiply -2 by 7

-14+6

Add

y=-8

Answer 2

The resulting equation after substitution is

5x + 4(-2x + 6) = 3

quite literally you replaced y with what it equals (as said in the second equation)

you then distribute the 4 within the parenthesis

5x + -8x + 24 = 3

You make it easier

5x - 8x +24 = 3

you combine like terms

-3x + 24 = 3

you subtract 24 from both sides

-3x = -21

you divide both sides by -3

meaning x = 7

you then use that value x = 7 and substitude it for the x in the other equation.

That makes the y equation

y = -2(7) + 6

you then solve

y = -14+6

y = 6 - 14

y = -8