Solve the system of equations. −4x+6y=38 x−5y=−20 (1 point) Responses (35, −3) left parenthesis 35 comma negative 3 right parenthesis (−5, 3) left parenthesis negative 5 comma 3 right parenthesis (5, 3) left parenthesis 5 comma 3 right parenthesis (−35, −3

1 answer

To solve the system of equations:

  1. \(-4x + 6y = 38\) (Equation 1)
  2. \(x - 5y = -20\) (Equation 2)

We'll use the substitution or elimination method. Let's solve Equation 2 for \(x\):

From Equation 2: \[ x = 5y - 20 \]

Now, substitute this expression for \(x\) in Equation 1:

\[ -4(5y - 20) + 6y = 38 \]

Distribute \(-4\): \[ -20y + 80 + 6y = 38 \]

Combine like terms: \[ -20y + 6y + 80 = 38 \] \[ -14y + 80 = 38 \]

Now, isolate \(y\): \[ -14y = 38 - 80 \] \[ -14y = -42 \] \[ y = \frac{-42}{-14} = 3 \]

Now that we have \(y\), substitute back to find \(x\): \[ x = 5(3) - 20 \] \[ x = 15 - 20 \] \[ x = -5 \]

So, the solution to the system of equations is: \[ (x, y) = (-5, 3) \]

The correct response from the options given is: \[ \text{(−5, 3)} \]