Question

Question
Solve the system of equations using your Desmos calculator:

3x+2y=2


−2x+y=8


(1 point)
Responses

(14, -20)
(14, -20)

(-2, 4)
(-2, 4)

(4, -2)
(4, -2)

(-4, 2)
(-4, 2)

Answer 1

To solve the system of equations:

1. \(3x + 2y = 2\)
2. \(-2x + y = 8\)

You can use the method of substitution or elimination, or you can graph the equations to find the intersection.

First, let's solve the second equation for \(y\):
\[
y = 2x + 8
\]

Now, substitute \(y\) in the first equation:
\[
3x + 2(2x + 8) = 2
\]

Expanding this:
\[
3x + 4x + 16 = 2
\]
\[
7x + 16 = 2
\]
\[
7x = 2 - 16
\]
\[
7x = -14
\]
\[
x = -2
\]

Now, substitute \(x = -2\) back into the equation for \(y\):
\[
y = 2(-2) + 8 = -4 + 8 = 4
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (-2, 4)
\]

So the answer from the options provided is:

**(-2, 4)**