Question

Solve the system of equations minus, 6, x, plus, 2, y, equals, minus, 14−6x+2y=−14 and minus, 5, x, plus, 5, y, equals, 5−5x+5y=5 by combining the equations.
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.
5
5 left parenthesis, minus, 6, x(−6x plus, 2, y+2y equals= minus, 14, right parenthesis−14)
2
2 left parenthesis, minus, 5, x(−5x plus, 5, y+5y equals= 5, right parenthesis5)
minus, 30, x−30x plus, 10, y+10y equals= minus, 70−70
minus, 10, x−10x plus, 10, y+10y equals= 1010
xx plus+
yy equals=
Answer
Attempt 1 out of 5
You must answer all questions above in order to submit.

Answer 1

To solve the system of equations:

1. \(-6x + 2y = -14\)
2. \(-5x + 5y = 5\)

we'll combine these equations.

First, we will multiply the equations by suitable constants to facilitate elimination. Let's choose to eliminate \(y\).

**Step 1: Multiply the equations.**

For the first equation, we can multiply it by \(5\) (to match the coefficient of \(y\) in the second equation):

\[
5(-6x + 2y) = 5(-14)
\]

This simplifies to:

\[
-30x + 10y = -70 \quad \text{(Equation 3)}
\]

For the second equation, we can multiply it by \(2\):

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

This simplifies to:

\[
-10x + 10y = 10 \quad \text{(Equation 4)}
\]

**Step 2: Subtract the equations to eliminate \(y\)**.

Now, we will subtract Equation 4 from Equation 3:

\[
(-30x + 10y) - (-10x + 10y) = -70 - 10
\]

This simplifies to:

\[
-30x + 10y + 10x - 10y = -80
\]

Which simplifies further to:

\[
-20x = -80
\]

**Step 3: Solve for \(x\)**.

Dividing both sides by \(-20\):

\[
x = 4
\]

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

Now we'll substitute \(x = 4\) back into one of the original equations. We can use the first equation:

\[
-6(4) + 2y = -14
\]

Which simplifies to:

\[
-24 + 2y = -14
\]

Adding 24 to both sides gives us:

\[
2y = 10
\]

Dividing both sides by \(2\):

\[
y = 5
\]

**Final Solution**: \((x, y) = (4, 5)\).

Thus, the solution to the system of equations is:

\[
x = 4, \quad y = 5
\]