Question

Solve the system of equations 7, x, minus, 7, y, equals, minus, 217x−7y=−21 and x, minus, 3, y, equals, 7x−3y=7 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.
left parenthesis, 7, x(7x minus, 7, y−7y equals= minus, 21, right parenthesis−21)
left parenthesis, x(x minus, 3, y−3y equals= 7, right parenthesis7)
7, x7x minus, 7, y−7y equals= minus, 21−21
xx minus, 3, y−3y equals= 77
0
0xx plus+
0
0yy equals=
Answer
Attempt 1 out of 5

Answer 1

To solve the system of equations given by:

1. \( 7x - 7y = -21 \)
2. \( x - 3y = 7 \)

we can manipulate and combine these equations to solve for \( x \) and \( y \). Let's simplify the equations and solve the system step by step.

### Step 1: Simplify the first equation

The first equation can be simplified:

\[
7x - 7y = -21
\]

Dividing the entire equation by 7 gives:

\[
x - y = -3 \quad (1)
\]

### Step 2: Keep the second equation as is

The second equation remains:

\[
x - 3y = 7 \quad (2)
\]

### Step 3: Rearranging Equation (1)

From equation (1), we can express \( x \) in terms of \( y \):

\[
x = y - 3 \quad (3)
\]

### Step 4: Substitute equation (3) into equation (2)

Now we substitute \( x \) from equation (3) into equation (2):

\[
(y - 3) - 3y = 7
\]

### Step 5: Solve for \( y \)

Rearranging gives:

\[
y - 3 - 3y = 7
\]
\[
-2y - 3 = 7
\]
\[
-2y = 10
\]
\[
y = -5
\]

### Step 6: Substitute \( y \) back to find \( x \)

Now, we substitute \( y = -5 \) back into equation (3) to find \( x \):

\[
x = (-5) - 3 = -8
\]

### Solution

The solution to the system of equations is:

\[
x = -8, \quad y = -5
\]

This means that the final answer is \( (x, y) = (-8, -5) \).