Question

Solve the equations using cross multiplication method: $3x+2y=10$ and $4x-2y=4$

• A. $x=-2,y=2$
• B. $x=2,y=-2$
• C. $x=-2,y=-2$
• D. $x=2,y=2$

Answer 1

The correct option is D $x=2,y=2$

$3x+2y=10$---(1)
$4x-2y=4$---(2)
Using formula for cross multiplication method:
$\frac{x}{(b_1{c}_2-b_2{c}_1)}=\frac{y}{(c_1{a}_2-a_1{c}_2)}=\frac{-1}{(a_1{b}_2-a_2{b}_1)}$
So, from equation (1) and (2) we can write the value of $a,b$ and $c$.
$\frac{x}{2\times 4-(-2)\times 10}=\frac{y}{10\times 4-3\times 4}=\frac{-1}{3\times (-2)-4\times 2}$
$\frac{x}{8+20}=\frac{y}{40-12}=\frac{-1}{-6-8}$
$\frac{x}{28}=\frac{y}{28}=\frac{-1}{-14}$
$\frac{x}{28}=\frac{-1}{-14}$
$-14x=-28$
$x=2$
$\frac{y}{28}=\frac{-1}{-14}$
$-14y=-28$
$y=2$
Therefore, $x=2,y=2$