Question

Part A: Solve the following system of equations algebraically showing your work: 3x + 2y + 4 and 4x +3y = 7 Part B: Describe which method you used to solve the system. Explain why that method was better than the other methods.

Answer 1

(-2, 5)

Explanation:

3x + 2y = 4

4x +3y = 7

x = (2·7 -3·4)/(2·4 -3·3) = 2/-1 = -2

y = (4·4 -7·3)/-1 = -5/-1 = 5

The solution is (x, y) = (-2, 5).

_____

I used the Vedic maths variation of Cramer's Rule, because it is straightforward, and because the usual methods of elimination or substitution get messy with these coefficients.

Cramer's Rule gives you a formula for the values of x and y in the system

• ax +by = c
• dx +ey = f

The formula is ...

• ∆ = ae -db
• x = (ce -fb)/∆
• y = (fa -db)/∆

The Vedic maths variation of this negates each of the terms, which has the effect of putting the products into X patterns that are relatively easy to memorize.