Solve the system of equations. −4x+6y=38 x−5y=−20 (1 point)

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

We can use the substitution or elimination method. Let's use the substitution method.

From the second equation, solve for \(x\):

\[ x = 5y - 20 \]

Now substitute \(x\) into the first equation:

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

Distributing gives:

\[ -20y + 80 + 6y = 38 \]

Combining like terms:

\[ -14y + 80 = 38 \]

Subtract 80 from both sides:

\[ -14y = 38 - 80 \] \[ -14y = -42 \]

Divide by -14:

\[ y = \frac{-42}{-14} = 3 \]

Now substitute \(y\) back into the equation for \(x\):

\[ x = 5(3) - 20 \] \[ x = 15 - 20 \] \[ x = -5 \]

So, the solution to the system of equations is:

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

Therefore, the answer is \((−5, 3)\).