To find the solution to the system of linear equations given by:
- \( y = -3x + 2 \)
- \( y = x - 6 \)
We can set the two equations equal to each other since both expressions represent \( y \):
\[ -3x + 2 = x - 6 \]
Now, let's solve for \( x \):
- Add \( 3x \) to both sides:
\[ 2 = 4x - 6 \]
- Add \( 6 \) to both sides:
\[ 8 = 4x \]
- Divide both sides by \( 4 \):
\[ x = 2 \]
Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the second equation:
\[ y = 2 - 6 \] \[ y = -4 \]
Thus, the solution to the system of equations is \( (2, -4) \).
Checking with the first equation:
\[ y = -3(2) + 2 = -6 + 2 = -4 \]
Both equations give \( y = -4 \) when \( x = 2 \), confirming the solution.
The answer is \( \boxed{(2, -4)} \).
1 answer