Solve for x and y: 2x - 3y = 13, 7x - 2y = 20

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Solve for x and y:
2x – 3y = 13,
7x – 2y = 20

Solve for x and y:
2x – 3y = 13,
7x – 2y = 20

Solution:

The given system of eq. is:
$\begin{array}{cc} 2 \mathrm{x}-3 \mathrm{y}=13 & \ldots \ldots \text { (i) } \\ 7 \mathrm{x}-2 \mathrm{y}=20 & \ldots \ldots \text { (ii) } \end{array}$
When multiplying equation(i) by 2 and equation(ii) by 3 , we obtain:
$4 \mathrm{x}-6 \mathrm{y}=26 \quad \ldots \ldots \text { (iii) }$
$21 \mathrm{x}-6 \mathrm{y}=60 \ldots \ldots \text {..(iv) }$
On subtracting equation(iii) from equation(iv) we obtain:
$\begin{array}{l} 17 \mathrm{x}=(60-26)=34 \\ \Rightarrow \mathrm{x}=2 \end{array}$
On substituting the value of $\mathrm{x}=2$ in equation(i), we obtain:
$\begin{array}{l} 4-3 y=13 \\ \Rightarrow 3 y=(4-13)=-9 \\ \Rightarrow y=-3 \end{array}$
As a result, the solution is $\mathrm{x}=2$ and $\mathrm{y}=-3$ .