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Pair of Linear Equations in Two variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables5 Marks
Question
Check graphically, whether the pair of sequence is consistent. If so, then solve them graphically.
$\begin{array}{l}x+3 y=6 \\2 x-3 y=12\end{array}$
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Answer

$\begin{array}{r}x+3 y=6 \quad \quad \ldots \ldots(1) \\2 x-3 y=12 \quad \quad \ldots \ldots(2)\end{array}$
Solving equation 1,
We have $x+3 y=6$
$\Rightarrow 3 y=6-x$
When $x=0$, we have, $y=2$
When $x=3$, we have, $y=1$
Solving equation 2,
We have, $2 x-3 y=12$
$\Rightarrow y=\frac{2 x-12}{3}$
When $x=3$, we have, $y=-2$
When $x=6$, we have, $y=0$
Hence, plotting both equations on the graph,

Image
Since, from the graph it is clear that both the lines intersect at a common point $(6,0)$.
Hence, the given equations are consistent and the solution is $(6,0)$.

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