Question

how many solutions does this equation have?
-5x+y=-18
10x-2y=36

Answer 1

To determine the number of solutions for a system of equations, we need to solve the equations and see if they intersect at one point (one solution), are parallel (no solution), or overlap (infinitely many solutions).

Rearranging the first equation, we have:

y = 5x - 18

Substitute this value of y into the second equation:

10x - 2(5x - 18) = 36
10x - 10x + 36 = 36
36 = 36

As a result, this means that the second equation is satisfied by any value of x. Therefore, the system of equations has infinitely many solutions.