Question

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

y = -x + 6
y = 3x -2

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To estimate the solution to the system of linear equations, we can examine the graph.

The first equation, y = -x + 6, is a linear equation in slope-intercept form, where the slope is -1 and the y-intercept is 6. This means that the line will have a negative slope and will intersect the y-axis at (0, 6).

The second equation, y = 3x - 2, is also in slope-intercept form, with a slope of 3 and a y-intercept of -2. This line will have a positive slope and will intersect the y-axis at (0, -2).

To estimate the solution to the system, we need to find the point at which these two lines intersect, which represents the solution to the system of equations.

From the graph, we can see that the lines intersect at the point where they cross each other. In this case, the lines intersect at approximately (2, 4).

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