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Estimate the solution to the system of these linear equations based on the graph. y=−5x+7 y=−2x+10 (1 point)

(−1, 12)

(−1,−12)

(1,−12)

(12,−1)

1 answer

To estimate the solution to the system of the linear equations \(y = -5x + 7\) and \(y = -2x + 10\), we can find the point where the two lines intersect.

  1. Set the two equations equal to each other: \[ -5x + 7 = -2x + 10 \]

  2. Rearranging gives: \[ -5x + 2x = 10 - 7 \] \[ -3x = 3 \] \[ x = -1 \]

  3. Substitute \(x = -1\) into one of the original equations to find \(y\). Using the first equation: \[ y = -5(-1) + 7 = 5 + 7 = 12 \]

So the solution to the system is \((-1, 12)\), which corresponds to the first option:

\((−1, 12)\).