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Linear Equations in Two Variables — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsLinear Equations in Two Variables4 Marks
Question
Form the pair of linear equations in the following problems, and find their solution graphically:
$5$ pencils and $7$ pens together cost Rs. $50$, whereas $7$ pencils and $5$ pens together cost Rs. $46.$ Find the cost of one pencil and a pen.
✓

Answer

Let the number of pencils and pens be $x$ and $y$ respectively.
According to questions.
$5x + 7y = 50 .......(i)$
$7x + 5y = 46 ........(ii)$
From (i), $\text{y}=\frac{50-5\text{x}}{7}\ ......(\text{iii})$
Putting $x = 3$ in $(iii)$, we get $Y = 5$
Putting $x = -4$ in $(iii)$, we get $Y = 10$
$x$
$3$
$-4$
$Y$
$5$
$10$


From $(ii)$, $\text{y}=\frac{46-7\text{x}}{5}\ ......(\text{iv})$
Putting $x = 3$ in $(iv)$, we get $y = 5$
Putting $x = -2$ in $(iv)$, we get $y = 12$
$x$
$3$
$-2$
$y$
$5$
$12$
Thus, from graph cost of pencil $= Rs. 3$ and cost of pen$= Rs. 5.$

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