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Solve the system of equations.

x−3y=18

7x−5y=46
(1 point)
Responses

(3, −5)
left parenthesis 3 comma negative 5 right parenthesis

(33, 5)
left parenthesis 33 comma 5 right parenthesis

(−3, −5)
left parenthesis negative 3 comma negative 5 right parenthesis

(105, 5)

1 answer

To solve the system of equations:

  1. \( x - 3y = 18 \) (Equation 1)
  2. \( 7x - 5y = 46 \) (Equation 2)

We'll solve it step by step.

First, let's solve Equation 1 for \( x \):

\[ x = 3y + 18 \]

Now, we substitute \( x \) in Equation 2 with \( 3y + 18 \):

\[ 7(3y + 18) - 5y = 46 \]

Expanding the equation:

\[ 21y + 126 - 5y = 46 \]

Combine like terms:

\[ 16y + 126 = 46 \]

Now, isolate \( y \):

\[ 16y = 46 - 126 \]

\[ 16y = -80 \]

\[ y = -5 \]

Now that we have \( y \), we can substitute it back into the expression for \( x \):

\[ x = 3(-5) + 18 \]

\[ x = -15 + 18 \]

\[ x = 3 \]

Thus, the solution to the system of equations is:

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

So the answer is \((3, -5)\).