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Solve the system of equations.

x=6y−3

2x+7y=13
(1 point)

3 answers

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.

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

y=10+4x
(1 point)

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.