Question

Solve the system by graphing.
3x-y=-1
y=-x+5
The solution is ( _ , _ )

Answer 1

The system of equations is solved by graphing both lines and finding the intersection point, which is determined to be (2, 3).

Step-by-step explanation:

To solve the system by graphing, you need to graph both equations and find the point where they intersect. The equations given are 3x-y=-1 and y=-x+5.

First, rearrange both equations into slope-intercept form (y = mx + b) to make them easier to graph.

• For the first equation, add y to both sides to get 3x = y - 1, and then add 1 to both sides to obtain y = 3x + 1.
• The second equation is already in slope-intercept form.

Now graph the lines on a coordinate plane:

1. For y = 3x + 1, plot the y-intercept (0, 1) and use the slope of 3 to plot another point (for example, from (0, 1) go up 3 units and right 1 unit to (1, 4)). Draw the line through these points.
2. For y = -x + 5, plot the y-intercept (0, 5) and use the slope of -1 to plot another point (for example, from (0, 5) go down 1 unit and right 1 unit to (1, 4)). Draw the line through these points.

Observe where the two lines intersect. Both lines intersect at the point (2, 3), so the solution to the system is (2, 3).