Estimate the solution to the system of these linear equations based on the graph.

Question

y = -5x + 7
y = -2x + 10 (1 point)
(12, -1)
(-1, 12)
(1, -12)
(-1, -12)

Answer 1

To estimate the solution to the system of linear equations given by:

1. \( y = -5x + 7 \)
2. \( y = -2x + 10 \)

you can find the point where these two lines intersect graphically.

Step 1: Identify y-intercepts

• For \( y = -5x + 7 \):

  • The y-intercept is (0, 7).

• For \( y = -2x + 10 \):

  • The y-intercept is (0, 10).

Step 2: Identify slopes

• The slope of the first line is -5, which means it goes down steeply.
• The slope of the second line is -2, which means it goes down less steeply than the first line.

Step 3: Estimate the point of intersection

You can also find the point of intersection algebraically by setting the two equations equal to each other:

\[ -5x + 7 = -2x + 10 \]

Solving the equation:

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

2. Substituting \( x = -1 \) back into either equation (let's use the second one): \[ y = -2(-1) + 10 = 2 + 10 = 12 \]

Thus, the point of intersection is \((-1, 12)\).

Conclusion

From the options provided:

• (12, -1)
• (-1, 12)
• (1, -12)
• (-1, -12)

The correct answer is (-1, 12).