Question

Find the value of $x$ and $y$ using cross multiplication method:
$3x+4y=43$ and $-2x+3y=11$

• A. $(7,2)$
• B. $(-7,7)$
• C. $(5,7)$
• D. $(-6,-7)$

Answer 1

Answer: (C)

$(5,7)$

$3x+4y=43$ ----- (1)

$-2x+3y=11$ ----- (2)

First use formula for cross multiplication method:

$\frac{x}{b_1{c}_2-b_2{c}_1}=\frac{y}{c_1{a}_2-a_1{c}_2}=\frac{-1}{a_2{b}_2-a_2{b}_1}$

So, from equation (1) and (2) we can write the value of a, b and c.

$\frac{x}{4\times 11-3\times 43}=\frac{y}{43\times (-2)-3\times 11}=\frac{-1}{3\times 3-(-2)\times 4}$

$\frac{x}{44-129}=\frac{y}{-86-33}=\frac{-1}{9+8}$

$\frac{x}{-85}=\frac{y}{-119}=\frac{-1}{17}$

$\frac{x}{-85}=\frac{-1}{17}$

$x=\frac{85}{17}=5$

$\frac{y}{-119}=\frac{-1}{17}$

$y=\frac{119}{17}=7$

The solution is $(5,7)$