Is (−2, 6) a solution to the system of these linear equations: x + 2y = 10 and 3x + y = 0 ? Why?

Answer 1

To check whether (−2, 6) is a solution to the system of linear equations x + 2y = 10 and 3x + y = 0, we need to substitute x = −2 and y = 6 into both equations and verify whether both sides of each equation are equal.

Substituting x = −2 and y = 6 into x + 2y = 10, we get:

−2 + 2(6) = 10
10 = 10

This equation is true, so (−2, 6) satisfies the first equation.

Substituting x = −2 and y = 6 into 3x + y = 0, we get:

3(−2) + 6 = 0
0 = 0

This equation is also true, so (−2, 6) satisfies the second equation.

Since (−2, 6) satisfies both equations in the system, it is a solution to the system of linear equations.