Questions: Solve the system by substitution. -x-5y = -20 6x = y+27 Select the correct choice below and, if necessary, fill in the answer box to complete your A. There are a finite number of solutions. The solution set is . (Simplify your answer. Type an ordered pair.)

Solve the system by substitution. -x-5y = -20 6x = y+27 Select the correct choice below and, if necessary, fill in the answer box to complete your A. There are a finite number of solutions. The solution set is . (Simplify your answer. Type an ordered pair.)
Transcript text: Solve the system by substitution. \[ \begin{aligned} -x-5 y & =-20 \\ 6 x & =y+27 \end{aligned} \] Select the correct choice below and, if necessary, fill in the answer box to complete your A. There are a finite number of solutions. The solution set is $\square$ \}. (Simplify your answer. Type an ordered pair.)
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Solution

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Solution Steps

To solve the system of equations by substitution, follow these steps:

  1. Solve one of the equations for one variable in terms of the other.
  2. Substitute this expression into the other equation.
  3. Solve the resulting equation for the remaining variable.
  4. Substitute back to find the value of the first variable.
Step 1: Solve for \( y \)

From the second equation \( 6x = y + 27 \), we can isolate \( y \): \[ y = 6x - 27 \]

Step 2: Substitute \( y \) into the first equation

Substituting \( y = 6x - 27 \) into the first equation \( -x - 5y = -20 \): \[ -x - 5(6x - 27) = -20 \] This simplifies to: \[ -x - 30x + 135 = -20 \] Combining like terms gives: \[ -31x + 135 = -20 \]

Step 3: Solve for \( x \)

Rearranging the equation: \[ -31x = -20 - 135 \] \[ -31x = -155 \] Dividing both sides by \(-31\): \[ x = 5 \]

Step 4: Substitute \( x \) back to find \( y \)

Now substituting \( x = 5 \) back into the expression for \( y \): \[ y = 6(5) - 27 = 30 - 27 = 3 \]

Final Answer

The solution set is \( (5, 3) \), so the answer is: \[ \boxed{(5, 3)} \]

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