To estimate the solution to the system of equations based on the given equations \( y = -5x + 7 \) and \( y = -2x + 10 \), we need to find the point where the two lines intersect.
Step 1: Finding the Intersection
The intersection point can be found by setting the two equations equal to each other:
\[ -5x + 7 = -2x + 10 \]
Step 2: Solve for \( x \)
Rearranging the equation:
\[ -5x + 2x = 10 - 7 \] \[ -3x = 3 \] \[ x = -1 \]
Step 3: Solve for \( y \)
Now we'll substitute \( x = -1 \) back into either of the original equations to find \( y \). We'll use the second equation:
\[ y = -2(-1) + 10 \] \[ y = 2 + 10 \] \[ y = 12 \]
Step 4: Write the Solution
The solution to the system of equations, which is the point of intersection, is:
\[ (x, y) = (-1, 12) \]
Summary
The estimated solution based on the system of equations is \( (-1, 12) \).
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