Question

Solve the system of equations.
x=6y−3

2x+7y=13
(1 point)

Answer 1

Solve the system of equations.
8x−3y= −22

y=10+4x
(1 point)

Answer 2

To solve the system of equations given by:

1. \( x = 6y - 3 \)
2. \( 2x + 7y = 13 \)

we can substitute equation (1) into equation (2).

Substituting \( x \) in equation (2):

\[
2(6y - 3) + 7y = 13
\]

Now, distribute \( 2 \):

\[
12y - 6 + 7y = 13
\]

Combine like terms:

\[
19y - 6 = 13
\]

Now, add \( 6 \) to both sides:

\[
19y = 19
\]

Now, divide by \( 19 \):

\[
y = 1
\]

Now that we have \( y \), we can substitute it back into equation (1) to find \( x \):

\[
x = 6(1) - 3
\]
\[
x = 6 - 3
\]
\[
x = 3
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (3, 1)
\]

To verify, substitute \( x = 3 \) and \( y = 1 \) into the second equation:

\[
2(3) + 7(1) = 6 + 7 = 13
\]

Since both equations are satisfied, the solution \( (3, 1) \) is correct.

Answer 3

To solve the system of equations:

1. \( 8x - 3y = -22 \)
2. \( y = 10 + 4x \)

we can substitute equation (2) into equation (1).

Substituting \( y \) in equation (1):

\[
8x - 3(10 + 4x) = -22
\]

Now, distribute \(-3\):

\[
8x - 30 - 12x = -22
\]

Combine like terms:

\[
-4x - 30 = -22
\]

Now, add \( 30 \) to both sides:

\[
-4x = 8
\]

Now, divide by \(-4\):

\[
x = -2
\]

Now that we have \( x \), substitute it back into equation (2) to find \( y \):

\[
y = 10 + 4(-2)
\]

Calculate \( y \):

\[
y = 10 - 8 = 2
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, 2)
\]

To verify, substitute \( x = -2 \) and \( y = 2 \) into the first equation:

\[
8(-2) - 3(2) = -16 - 6 = -22
\]

Since both equations are satisfied, the solution \( (-2, 2) \) is correct.