GG.8 Solve a system of equations using substitution

Question

J8X
Solve using substitution.

y = 4x + 3
y = x − 6

Answer 1

To solve the system of equations using substitution, we start with the two equations provided:

1. \( y = 4x + 3 \) (Equation 1)
2. \( y = x - 6 \) (Equation 2)

Since both equations are equal to \( y \), we can set them equal to each other:

\[ 4x + 3 = x - 6 \]

Now, we will solve for \( x \):

1. Subtract \( x \) from both sides: \[ 4x - x + 3 = -6 \] \[ 3x + 3 = -6 \]

2. Subtract 3 from both sides: \[ 3x = -6 - 3 \] \[ 3x = -9 \]

3. Divide both sides by 3: \[ x = -3 \]

Now that we have the value of \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use Equation 2:

\[ y = x - 6 \]

Substituting \( x = -3 \):

\[ y = -3 - 6 \] \[ y = -9 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (-3, -9) \]

In conclusion, the solution is:

\[ \boxed{(-3, -9)} \]