To estimate the solution to the system of linear equations based on the graph, we need to find the intersection point of the two lines.
Looking at the equations y = 5x + 10 and y = -2x + 3, we can see that both equations are given in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
For the first equation, y = 5x + 10, the slope is 5 and the y-intercept is 10.
For the second equation, y = -2x + 3, the slope is -2 and the y-intercept is 3.
Now, let's plot the two lines on a coordinate plane and find their intersection point:
1. Locate the y-intercept of the first equation by marking a point on the y-axis at y = 10.
2. Using the slope, plot a second point by moving up 5 units and right 1 unit from the y-intercept point.
3. Draw a straight line passing through the two points, representing the first equation.
4. Locate the y-intercept of the second equation by marking a point on the y-axis at y = 3.
5. Using the slope, plot a second point by moving down 2 units and right 1 unit from the y-intercept point.
6. Draw a straight line passing through the two points, representing the second equation.
The intersection point of the two lines represents the solution to the system of equations.
Based on the given answer choices, we can estimate the intersection point as (-1, 5), which means x = -1 and y = 5.
Thus, the estimated solution to the system of linear equations is (-1, 5).