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6x+2y=8



x+3y=−12


This system of equations is graphed. Find the solution to the system.

(1 point)
Responses

x=−3, y=−5
x=−3, y=−5

x=0, y=−4
x=0, y=−4

x=0, y=4
x=0, y=4

x=3, y=−5

1 answer

To solve the system of equations:

  1. \( 6x + 2y = 8 \)
  2. \( x + 3y = -12 \)

Let's solve the second equation for \( x \):

\[ x = -12 - 3y \]

Now we'll substitute this expression for \( x \) into the first equation:

\[ 6(-12 - 3y) + 2y = 8 \]

Distributing \( 6 \):

\[ -72 - 18y + 2y = 8 \]

Combining like terms:

\[ -72 - 16y = 8 \]

Now, isolate \( -16y \):

\[ -16y = 8 + 72 \] \[ -16y = 80 \]

Now divide by -16:

\[ y = \frac{80}{-16} = -5 \]

Now substitute \( y = -5 \) back into the expression for \( x \):

\[ x = -12 - 3(-5) \] \[ x = -12 + 15 \] \[ x = 3 \]

So, the solution to the system is:

\[ x = 3, y = -5 \]

Thus, the correct answer is:

x = 3, y = -5.