SOLUTION: Solve for x and y in terms of a and b where a ≠ b. bx + ay = -2a + b b^2x + a^2y = -ab

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Solve for x and y in terms of a and b where a ≠ b. bx + ay = -2a + b b^2x + a^2y = -ab      Log On


   

Question 257192: Solve for x and y in terms of a and b where a ≠ b.
bx + ay = -2a + b
b^2x + a^2y = -ab
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.bx+%2B+ay+=+-2a+%2B+b
2.b%5E2%2Ax+%2B+a%5E2%2Ay+=+-ab
Use eq. 1 to solve for x,
bx+%2B+ay+=+b-2a
bx=+b-2a-ay
b%5E2x=+b%5E2-2ab-aby
Subsitute into eq. 2 and solve for y,
2.b%5E2%2Ax+%2B+a%5E2%2Ay+=+-ab
b%5E2-2ab-aby+%2B+a%5E2%2Ay+=+-ab
y%28a%5E2-ab%29+=+ab-b%5E2
y=+%28ab-b%5E2%29%2F%28a%5E2-ab%29+
y=+%28b%2Across%28%28a-b%29%29%29%2F%28a%2Across%28%28a-b%29%29%29+
y=+b%2Fa
Then use this to find x,
b%5E2x=+b%5E2-2ab-aby
b%5E2x=+b%5E2-2ab-ab%2A%28b%2Fa%29
b%5E2x=+b%5E2-2ab-b%5E2%29
b%5E2x=-2ab
x=-2%28a%2Fb%29