Question

Solve each of the following systems of equations by the method of cross-multiplication:
ax + by = a-b
bx – ay = a+b

Answer 1

Answer: Solving the system of equation using cross multiplication we get x= 1 and y= - 1

Step-by-step explanation:

Step 1:

ax+by - (a-b)=0

bx-ay - (a+b) =0

Step 2:

Using the rule of cross multiplication

x/[-b(a+b) - a(a-b)] =y/[-b(a-b) +a(a+b)] =1/[-a^2-b^2]

Step 3:

x/[-ab-b^2-a^2+ab] =y/[-ab+b^2+a^2+ab]=1/[-(a^2+b^2)]

Step 4:

x/-(a^2+b^2) = y/a^2+b^2=1/-(a^2+b^2)

Step 5:

x=1 ; y= - 1.