# How do you solve this system of equations #y= \frac { - 3} { 4} x , x - 4y = 32#?

##### 3 Answers

#### Explanation:

Given

[1]

[2]

Using [1] we can substitute

[3]

Simplifying [4]

[5]

Continuing the simplification:

[6]

Dividing both sides of [6] by

[7]

Using [7] we can substitute

[8]

Simplifying [8]

[9]

#### Explanation:

#color(red)(y)=-3/4xto(1)#

#x-4color(red)(y)=32to(2)#

#"substitute "y=-3/4x" in "(2)#

#rArrx-(4xx-3/4)=32#

#rArrx+3x=32#

#rArr4x=32#

#"divide both sides by 4"#

#rArrx=8#

#"substitute this value in "(1)#

#y=-3/4xx8=-6#

#color(blue)"As a check"#

#"substitute these values in "(2)#

#8+24=32larr" True"#

#rArr"point of intersection "=(8,-6)# graph{(y+3/4x)(y-1/4x+8)((x-8)^2+(y+6)^2-0.06)=0 [-12.49, 12.48, -6.25, 6.24]}

Substitution.

#### Explanation:

There are many ways to solve systems of equations. For this system:

it would be easiest to solve it with substitution since Equation (Eq.) 1 is already solved for

This is Eq 2:

If we plug in Eq. 1 into Eq. 2, we get:

Now we solved for the first variable. To solve for

So, the solution to the system of equations is:

To check this answer, you can plug in the

Eq 1 verification by plugging in the

Eq 2 verification by plugging in the