Question

Graph the system of equations below to find the solution.
y= -2x +7
y= 3x-8

Answer 1

To graph the system of equations, we first need to write them in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

For the first equation, y = -2x + 7, the slope is -2 and the y-intercept is 7.
For the second equation, y = 3x - 8, the slope is 3 and the y-intercept is -8.

Next, we can plot the y-intercepts on the y-axis. For the first equation, (0,7), the y-intercept is 7. For the second equation, (0,-8), the y-intercept is -8.

Now, we can find another point for each equation by using the slope. From the y-intercept of the first equation, we can go down 2 units and to the right 1 unit to get another point, (1,5). From the y-intercept of the second equation, we can go up 3 units and to the right 1 unit to get another point, (1,-5).

Plotting these points and connecting them with a line will give us the graph of each equation:

For the first equation, y = -2x + 7, the graph will be a line that goes through the points (0,7) and (1,5).
For the second equation, y = 3x - 8, the graph will be a line that goes through the points (0,-8) and (1,-5).

The solution to the system of equations is where these two lines intersect.

Here is the graph:

graph(D-8,8,-8,10,-2x+7,3x-8)