Question

Solve the system of equations using your Desmos calculator:

3x+2y=2

−2x+y=8

(1 point)
Responses

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

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

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

(-4, 2)
(-4, 2)
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Answer 1

To solve the system of equations:

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

We can either solve it graphically or algebraically. Here, I'll solve it algebraically.

From the second equation, we can express \( y \) in terms of \( x \):

\[
y = 2x + 8
\]

Now, we can substitute this expression for \( y \) into the first equation:

\[
3x + 2(2x + 8) = 2
\]

Expanding this gives:

\[
3x + 4x + 16 = 2
\]

Combining like terms:

\[
7x + 16 = 2
\]

Now, isolate \( x \):

\[
7x = 2 - 16
\]
\[
7x = -14
\]
\[
x = -2
\]

Now that we have \( x \), substitute back to find \( y \):

\[
y = 2(-2) + 8
\]
\[
y = -4 + 8
\]
\[
y = 4
\]

The solution to the system of equations is:

\[
(x, y) = (-2, 4)
\]

Therefore, the answer is \((-2, 4)\).