Question

Solve t/he system of linear equations given by x + y = 1 and ax − by = c, where a, b, c are real numbers. Note: The solution in this case will not be numbers but formulas containing a, b, and c. Need help ASAP!!

Answer 1

see explanation

Explanation:

Given the 2 equations

x + y = 1 → (1)

ax - by = c → (2)

In (1) subtract y from both sides

x = 1 - y → (3)

Substitute x = 1 - y into (2)

a(1 - y) - by = c ← distribute left side

a - ay - by = c ( subtract a from both sides )

- ay - by = c - a ( multiply through by - 1 )

ay + by = a - c ← factor out y from each term on the left side

y(a + b) = a - c ← divide both sides by (a + b)

y =
`(a-c)/(a+b)` ← substitute into (3)

x = 1 -
`(a-c)/(a+b)` =
`(a+b)/(a+b)` -
`(a-c)/(a+b)` =
`(a+b-a+c)/(a+b)` =
`(b+c)/(a+b)`