Question

Solve using cross multiplication method

3x – 4y = 10 and 8x + 5y = 11

• A. (-2,1)
• B. (2,-1)
• C. (-2,-1)
• D. (2,1)

Answer 1

The correct option is B

(2,-1)

Given equations : 3x – 4y = 10 and 8x + 5y = 11

$a_1=3,b_1=-4,c_1=-10$ and $a_2=8,b_2=5,c_2=-11$

x y 1

-4 -10 3 -4

5 - 11 8 5

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

$\Rightarrow$ $\frac{x}{44+50}$ = $\frac{y}{-80+33}$ = $\frac{1}{15+32}$

$\Rightarrow$ $\frac{x}{94}$ = $\frac{y}{-47}$ = $\frac{1}{47}$

$\Rightarrow$ $\frac{x}{94}$ = $\frac{1}{47}$ $\Rightarrow$ x = 2

$\Rightarrow$ $\frac{y}{-47}$ = $\frac{1}{47}$ $\Rightarrow$ y = -1