Question

Solve the equations using the cross multiplication method:

$3x+2y=10and4x-2y=4.$

Answer 1

Step 1: Rewrite the equation in standard form

$$\begin{gathered} 3x+2y-10=0.......\left(1\right) \\ 4x-2y-4=0.......\left(2\right) \end{gathered}$$

Step 2: Solve the equations using the cross multiplication method

$$\begin{gathered} XY1 \\ \left|\begin{array}{cccc}2& -10& 3& 2\\ -2& -4& 4& -2\end{array}\right| \end{gathered}$$

$\frac{x}{-8-20}=\frac{y}{-40+12}=\frac{1}{-6-8}$

$\frac{x}{-28}=\frac{y}{-28}=\frac{1}{-14}$

$$\begin{gathered} \Rightarrow x=\frac{-28}{-14}andy=\frac{-28}{-14} \\ \Rightarrow x=2andy=2 \end{gathered}$$

Hence, the solution of given pair of equations is $x=2andy=2$