Question

Please help and explain! Will be giving over 30+ points!

Consider the following pair of equations:

y = x + 4
y = −2x − 2

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answer 1

y= x +4
y= -2x - 2

x+4 = -2x - 2
subtract for from both sides to cancel the +4 on the left of the equation
x= -2x - 6
add 2x on both sides to cancel the -2x on the right side of the equation because we want our variables to be on the same side
x+2x = -6
combine the like terms, in this case it's the x and 2x
3x= -6
divide both sides by three
x= -2
now we can plug x in to one of the original equations. I like to choose the easier one which is y= x +4
y= (-2) + 4
y= 2

the answer in (x,y) form is (-2, 2)

Answer 2

Since y equals both, they are equal to each other.
x+4=-2x-2

First, isolate the x by subtracting 4 from both sides.
x+4=-2x-2
-4 -4
x=-2x-6
Second, move the x's to one side by adding the 2x to both sides
x=-2x-6
+2x +2x
Then divide both sides by the coefficient of x.
(3x)/3=(-6)/3
So X=-2 The plug in the -2 for the x in either of the original equations such as x+4
Y=-2+4
Which equals 2
X= -2, Y= 2