Question

Solve The Following:

$\frac{3}{2}x+\frac{5}{3}y=7$ and

$9-10y=14$

Answer 1

Step 1: Make the coefficient of $x$ same in both the equations.

$\frac{3}{2}x+\frac{5}{3}y=7$

Multiply with $6$ on both sides.

$$\begin{gathered} \frac{3}{2}x\times 6+\frac{5}{3}y\times 6=7\times 6 \\ \Rightarrow 9x+10y=42..................\left(1\right) \end{gathered}$$

$9-10y=14...................\left(2\right)$

Step 2: Add equation $1$ and equation $2$

$$\begin{gathered} 9x+10y=42 \\ 9x-10y=14 \\ -------- \\ 18x=56 \\ -------- \end{gathered}$$

$x=\frac{56}{18}=\frac{28}{9}$

Step 3: Substitute the value of $x$ in equation $1$ to find $y$

$$\begin{gathered} 9\left(\frac{28}{9}\right)+10y=42 \\ 28+10y=42 \\ 10y=42-28 \\ 10y=14 \\ y=\frac{14}{10} \\ y=1.4 \end{gathered}$$

Hence, the value of $x$ and $y$ is $\frac{28}{9}$ and$1.4$ respectively.