Question

Solve $8x+5y=9,3x+2y=4$by any method.

Answer 1

Given two equations are

$$\begin{gathered} 8x+5y=9...\left(i\right) \\ 3x+2y=4...\left(ii\right) \end{gathered}$$

Step 1: Multiplying the equations $\left(i\right),\left(ii\right)$ by $3,8$ respectively.

In order to make the coefficients of $x$ equal multiply the equation $8x+5y=9$ by $3$and equation $3x+2y=4$ by $8$

Then we get the equations

$$\begin{gathered} 24x+15y=27...\left(iii\right) \\ 24x+16y=32...\left(iv\right) \end{gathered}$$

Step 2: Subtracting the equation $\left(iii\right)$ from $\left(iv\right)$

Subtract Equation $\left(iii\right)$ from Equation $\left(iv\right)$ to eliminate $x$ , because the coefficients of $x$ are the same.

$$\begin{gathered} 24x+16y=32 \\ 24x+15y=27 \\ \underline{---} \\ \underline{0+y=5} \\ \Rightarrow y=5 \end{gathered}$$

Step 3: Using the value of $y$ to get $x$

Substituting this value of $y$ in the equation$8x+5y=9,$ we get

$$\begin{gathered} 8x+5y=9 \\ \Rightarrow 8x+5\left(5\right)=9 \\ \Rightarrow 8x+25=9 \\ \Rightarrow 8x=9–25 \\ \Rightarrow 8x=–16 \\ \Rightarrow x=-2 \end{gathered}$$

Hence, the solution of the equations is $x=-2$ and $y=5$.