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# Testing a solution to a system of equations

Sal checks whether (-1,7) is a solution of the system: x+2y=13 and 3x-y=-11. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Is ( -1, 7) is solution for the equations below. The first equation is x + 2y =13, second equation is 3x - y = -11, Inorder for -1,7 for solution for the system it needs to satisfy both equations. x = -1 and y = 7, need to satisfy both equations to be a solution. Lets try with the first equation. If x=-1 & y =7 we will test if it satisfies this equation. So we have -1 + 2x7 = 13 ?I put a ? because we don't know if it satisfies. -1 + 14 = 13 So 13 =13, so it satisfy the first equation. Now lets us look at the second equation. We have 3 ( -1) - 7 = -11 ? Put ? as i don't know if it satisfies. -3 - 7 = -11? -3 -7 = -10. So we get -10 = -11, no It is not true. So x = -1 & y=7 does not satisfy the second equation. This over here is not a solution for the system. The answer is No as it satisfies the first equation, but not the second.