Question

Solve the system of linear equations using the matrix method.

4x – 3y = 3

3x – 5y = 7

Answer 1

`[(4,-3),(3,-5)] [(x),(y)] = [(3),(7)]` AX = B

A = `[(4,-3),(3,-5)]`

X = `[(x),(y)]` and B = `[(3),(7)]`

Now, |A| = `[(4,-3),(3,-5)]`

= −20 + 9

= −11 ≠ 0

⇒ A⁻¹ exists and hence the given equation has a unique solution.

∴ Adj A = `[(-5,-3),(3,4)]^T = [(-5,3),(-3,4)]`

and A⁻¹ = `1/|A|` (Adj A)

= `1/-11 [(-5,3),(-3,4)]`

X = A⁻¹B

⇒ `[(x),(y)] = 1/11 [(-5,-3),(3,4)] [(3),(7)]`

= `[(-6/11),(-19/11)]`

So, x = `-6/11`, y = `-19/11`