To estimate the solution to the system of linear equations given by:
- \( y = -x + 6 \)
- \( y = 3x - 2 \)
you can find the point where the two lines intersect. This intersection point is the solution to the system of equations.
To do this algebraically, set the two equations equal to each other:
\[ -x + 6 = 3x - 2 \]
Now, solve for \( x \):
- Add \( x \) to both sides:
\[ 6 = 4x - 2 \]
- Add 2 to both sides:
\[ 8 = 4x \]
- Divide by 4:
\[ x = 2 \]
Now that we have the value of \( x \), substitute it back into either equation to find \( y \). We'll use the first equation \( y = -x + 6 \):
\[ y = -2 + 6 = 4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (2, 4) \]
The estimated point of intersection of the two lines, based on the graph, is approximately \((2, 4)\).