for what values of the coefficient "a" and "b" is (2, -1) the solution to the following system? ax + by = -7 2ax - 3by = 1

Question

for what values of the coefficient "a" and "b" is (2, -1) the solution to the following system?

ax + by = -7

2ax - 3by = 1

Answer 1

plug (2,-1) = (a,b) = (x,y) into the equation ax+by=-7 and 2ax-3by=1 to get

2a -b =-7 and

4a +3b = 1

multiply first by 2 to get

4a-2b =-14, the subtract 2nd to get

-5b = 15

b =-3

2a -(-3) = -7

2a =-10

a =-5

a=-5, b =-3

x=2, y=-1

That's a solution to the 2 equations, (a,b) = (-5,-3) and (x,y) = (2,-1)