Question

Use substitution to solve the system.

x=3y-8
3x-4y=-9

Answer 1

Equation 1) x = 3y - 8
Equation 2) 3x - 4y = -9

For equation 1, subtract 3y from both sides.

1) x - 3y = -8

Then, multiply ALL of equation 1 by 3.

1) 3(x - 3y = -8)

1) 3x - 9y = -24
2) 3x - 4y = -9

Subtract equations from one another.

-5y = -15

Divide both sides by -5.

y = 3

Plug in 3 for y in the second equation.

3x - 4y = -9

3x - 4(3) = -9

Simplify.

3x - 12 = -9

Add 12 to both sides.

3x = -9 + 12

Simplify.

3x = 3

x = 1

~Hope I helped!~

Answer 2

x=3y-8
3x-4y=-9

We are told that:
x=3y-8

So replace x in 3x-4y=-9 with x=3y-8 like so:
3(3y-8)-4y=-9

Start by distributing the 3:

`(3)(3y)+(3)(-8)+-4y=-9`
Now you have:

`9y+-24+-4y=-9`
Combine like terms, now you have:

`5y-24=-9`
add 24 to both sides

`5y-24+24=-9+24`
Now you have:

`5y=15`
Divide both sides by 5 to get:
y=3

Now that you know y=3 plug it into:
x=3y-8
x=3(3)-8
x=1

Final answer:
(1,3)