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P-1 Linear Equations in Two Variables — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-1 Linear Equations in Two Variables2 Marks
Question
Solve the following simultaneous equation.
$\frac{1}{3} x+y=\frac{10}{3} ; 2 x+\frac{1}{4} y=\frac{11}{4}$
✓

Answer


$\frac{1}{3} x + y =\frac{10}{3} \Rightarrow \frac{ x +3 y }{3}=\frac{10}{3} \Rightarrow x +3 y =10 \dots(I)$
$2 x +\frac{1}{4} y =\frac{11}{4} \Rightarrow \frac{8 x + y }{4}=\frac{11}{4} \Rightarrow 8 x + y =11\dots(II)$
Multiplying Eq. II by 3
$24 x+3 y=33 \ldots \text { (III) }$
Equating Eq. I and III, change the signs of Eq. III
$x+3y=10$
$\underline{-24x-3y=-33}$
$-23x=-23$
$x=1$
Substituting x = 1 in Eq. I
$1+3 y=10 $
$3 y=10-1 $
$ 3 y=9$
$ y=\frac{9}{3} $
$ y=3$
∴ solution is (x,y) = (1, 3)

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