Question

Estimate the solution to the system of these linear equations based on the graph
y = -x + 6
y = 3x -2

Answer 1

To estimate the solution to the system of linear equations, we need to find the point of intersection on the graph.

First, we can rewrite the equations in slope-intercept form:

y = -x + 6 is equivalent to y = -1x + 6
y = 3x - 2

Now let's plot the graph:

The first equation has a y-intercept of 6 and a slope of -1. This means that for every unit increase in x, y will decrease by 1.

The second equation has a y-intercept of -2 and a slope of 3. This means that for every unit increase in x, y will increase by 3.

Now we can plot the two lines on the graph:

(Insert graph of y = -x + 6 and y = 3x - 2)

From the graph, we can see that the lines intersect at the point (2,4) or (2.0,4.0).

Therefore, the estimated solution to the system of linear equations is x = 2 and y = 4.