Determine the number of solutions to this system of linear equations: y=x+5 y=−x+5

Answer 1

The two equations are y = x + 5 and y = -x + 5.

To determine the number of solutions to this system of linear equations, we can graph the two lines represented by these equations.

The first equation, y = x + 5, has a slope of 1 and a y-intercept of 5. So, one point on this line is (0, 5).

The second equation, y = -x + 5, has a slope of -1 and a y-intercept of 5. So, one point on this line is also (0, 5).

When we graph these lines, we see that they intersect at the point (0, 5).

Therefore, there is only one solution to this system of linear equations.