Question

Determine the number of solutions to this system of linear equations:
y=x+5
y=−x+5 (1 point)

Answer 1

try again

Answer 2

There is only one solution for this system of linear equations.
y=x+5
y=−x+5

Substitute the first equation into the second equation:
x+5 = -x+5

Rearranging the terms:
x + x = 0
2x = 0
x = 0

Now, substitute the value of x back into the first equation to find y:
y = 0 + 5
y = 5

Therefore, the solution to the system of linear equations is x = 0 and y = 5.

Answer 3

Since both equations are in the form y = mx + b, where m is the slope and b is the y-intercept, we can see that they have the same y-intercept of 5 but different slopes of 1 and -1 for the first and second equations respectively.

Since the lines have different slopes, they are not parallel and will intersect at a single point.

Therefore, there is one unique solution for this system of linear equations.