Solve : 15x + 17y = 21; 17x + 15y = 11 - Vidyadip

Question

Solve : 15x + 17y = 21; 17x + 15y = 11

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Answer

$\begin{gathered}
15 x+17 y=21 \ldots \text { (I) } \\
17 x+15 y=11 \ldots \text { (II) }
\end{gathered}$
In the two equations above, the coefficients of $x$ and $y$ are interchanged. While solving such equations we get two simple equations by adding and subtracting the given equations. After solving these equations, we can easily find the solution.
Let's add the two given equations.
$\begin{aligned}
15 x+17 y & =21 \\
+17 x+15 y & =11 \\
\hline 32 x+32 y & =32
\end{aligned}$
Dividing both sides of the equation by 32 .
$x+y=1 \ldots \text {(III)}$
Now, let's subtract equation (II) from (I)
$\begin{aligned}
& \quad 15 x+17 y=21 \\
& \begin{array}{r}
+ \_17 x \pm 15 y=\_11 \\
\hline-2 x+2 y=10
\end{array} \\
\end{aligned}$
dividing the equation by 2 .
$-x+y=5 \ldots \text { (IV) }$
Now let's add equations (III) and (V).
$\begin{aligned}
& \quad x+y=1 \\
+ & -x+y=5 \\
& \hline \therefore \quad 2 y=6 \\
& \therefore \quad y=3 \\
\end{aligned}$
Place this value in equation (III).
$\begin{array}{ll}
x+y=1 \\
\therefore x+3=1 \\
\therefore x=1-3 \quad \therefore x=-2 \\
(x, y)=(-2,3) \text { is the solution. }
\end{array}$

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