Answer:
see explanation
Step-by-step 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 = [tex]\frac{a-c}{a+b}[/tex] ← substitute into (3)
x = 1 - [tex]\frac{a-c}{a+b}[/tex] = [tex]\frac{a+b}{a+b}[/tex] - [tex]\frac{a-c}{a+b}[/tex] = [tex]\frac{a+b-a+c}{a+b}[/tex] = [tex]\frac{b+c}{a+b}[/tex]
