Question

What is the solution to y = x + 2 and y = 3x – 2 and how do you know? PLEASE HELPPPPP! THANK U!

Answer 1

(2,4)

Explanation:

We have the system:

y=x+2

y=3x-2.

This is already setup for substitution.

I'm going to replace my first y with what the second y equals.

That is, I'm going to write 3x-2=x+2.

Time to solve the following for x:

3x-2=x+2

Subtract x on both sides:

2x-2= 2

Add 2 on both sides:

2x. = 4

Divide both sides by 2:

x. = 2

Now that we know x=2 and we have an equation that relates x to y: either y=x+2 or y=3x-2, doesn't matter which we use, we can find y.

So we y=x+2 with x=2 which means y=2+2=4.

So the solution, the intersection, is (2,4).

Answer 2

(2, 4 )

Explanation:

Given the 2 equations

y = x + 2 → (1)

y = 3x - 2 → (2)

Substitute y = 3x - 2 into (1)

3x - 2 = x + 2 ( subtract x from both sides )

2x - 2 = 2 ( add 2 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Substitute x = 2 into (1) for the corresponding value of y

y = x + 2 = 2 + 2 = 4

As a check

Substitute x = 2 into the 2 equations and check validity

(1) → y = 2 + 2 = 4 ← Correct

(2) → y = (3 × 2) - 2 = 6 - 2 = 4 ← Correct

Solution is (2, 4 )