Solve the system of equations minus, 2, x, minus, 7, y, equals, minus, 14−2x−7y=−14 and minus, x, minus, 5, y, equals, minus, 13−x−5y=−13 by combining the equations.

Question

Below, two sets of the two equations are shown. The first set has input boxes in front of each equation to put a number to multiply it by. When you enter a number, the corresponding equation below changes to be the result of the multiplication. Under the second set, a resulting equation is shown with input boxes for the coefficients and constant. Then, there is a "try" button. When you press the try button, if your answer is correct, it will be placed on the page and a new question will appear with a new input box. This process will continue until the final answer area appears with the submit button.
left parenthesis, minus, 2, x(−2x minus, 7, y−7y equals= minus, 14, right parenthesis−14)
left parenthesis, minus, x(−x minus, 5, y−5y equals= minus, 13, right parenthesis−13)
minus, 2, x−2x minus, 7, y−7y equals= minus, 14−14
minus, x−x minus, 5, y−5y equals= minus, 13−13
0
0xx plus+
0
0yy equals=

Answer 1

To solve the system of equations by combining them, we will first rewrite the two equations:

1. \( -2x - 7y = -14 \) (Equation 1)

2. \( -x - 5y = -13 \) (Equation 2)

Next, we can manipulate these equations to eliminate one of the variables. Let's first multiply Equation 2 by 2 to align the coefficients of \( x \):

\[ 2(-x - 5y) = 2(-13) \]

This gives us:

\[ -2x - 10y = -26 \quad (Equation 3) \]

Now we have the system:

1. \( -2x - 7y = -14 \)

2. \( -2x - 10y = -26 \)

Now we can eliminate \( -2x \) from both equations. We do this by subtracting Equation 1 from Equation 3:

\[ (-2x - 10y) - (-2x - 7y) = -26 - (-14) \]

This simplifies to:

\[ -10y + 7y = -26 + 14 \]

So, we get:

\[ -3y = -12 \]

Now, divide both sides by -3:

\[ y = 4 \]

Now that we have \( y \), we can substitute it back into one of the original equations to find \( x \). Let's substitute \( y = 4 \) into Equation 1:

\[ -2x - 7(4) = -14 \]

This simplifies to:

\[ -2x - 28 = -14 \]

Adding 28 to both sides gives:

\[ -2x = 14 \]

Dividing by -2, we find:

\[ x = -7 \]

So, the solution to the system of equations is:

\[ x = -7, \quad y = 4 \]

The final answer is:

\[ (x, y) = (-7, 4) \]