To solve the system of equations given:
- \( y = 5x + 6 \) (Equation 1)
- \( x = 23 - 2y \) (Equation 2)
We can start by substituting Equation 1 into Equation 2.
- From Equation 1, we have \( y = 5x + 6 \).
- Substitute this expression for \( y \) into Equation 2:
\[ x = 23 - 2(5x + 6) \]
Now, simplify the equation:
\[ x = 23 - 10x - 12 \]
Combine like terms:
\[ x = 11 - 10x \]
Next, add \( 10x \) to both sides:
\[ x + 10x = 11 \]
This simplifies to:
\[ 11x = 11 \]
Now divide both sides by 11:
\[ x = 1 \]
Now that we have the value of \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ y = 5(1) + 6 \] \[ y = 5 + 6 = 11 \]
So, the values are:
\[ x = 1 \] \[ y = 11 \]
Feel free to enter these values into Zearn!