Questions: Solve graphically. x+y = 12 5x+y = 0 What is the solution of the system of equations? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is one solution. The solution is . (Type an ordered pair.) B. There are infinitely many solutions of the form ( x, ). (Use integers or fractions for any numbers in the expression.) C. The system of equations has no solution.

Solve graphically. x+y = 12 5x+y = 0 What is the solution of the system of equations? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is one solution. The solution is . (Type an ordered pair.) B. There are infinitely many solutions of the form ( x, ). (Use integers or fractions for any numbers in the expression.) C. The system of equations has no solution.
Transcript text: Solve graphically. \[ \begin{aligned} x+y & =12 \\ 5x+y & =0 \end{aligned} \] What is the solution of the system of equations? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is one solution. The solution is $\square$ $\square$. (Type an ordered pair.) B. There are infinitely many solutions of the form ( x, ). (Use integers or fractions for any numbers in the expression.) C. The system of equations has no solution.
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Solution

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Solution Steps

Step 1: Rewrite the system of equations

The given system of equations is: \[ \begin{aligned} x + y &= 12 \\ 5x + y &= 0 \end{aligned} \]

Step 2: Solve for \( y \) in both equations

From the first equation: \[ y = 12 - x \]

From the second equation: \[ y = -5x \]

Step 3: Set the two expressions for \( y \) equal to each other

\[ 12 - x = -5x \]

Step 4: Solve for \( x \)

Add \( 5x \) to both sides: \[ 12 + 4x = 0 \]

Subtract \( 12 \) from both sides: \[ 4x = -12 \]

Divide both sides by \( 4 \): \[ x = -3 \]

Step 5: Substitute \( x = -3 \) back into one of the equations to find \( y \)

Using \( y = 12 - x \): \[ y = 12 - (-3) = 15 \]

Final Answer

The solution to the system of equations is: \[ \boxed{(-3, 15)} \]

The correct choice is: A. There is one solution. The solution is \(\boxed{(-3, 15)}\).

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