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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1 answer

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 \((-2, 4)\).