Solve the following simultaneous equation. 99x + 101 y = 499; 101… - Vidyadip

Question

Solve the following simultaneous equation.
99x + 101 y = 499; 101x + 99y = 501

✓

Answer

$99 x+101 y=499 \ldots(I) $
$101 x+99 y=501 \ldots(II)$
Adding both the Equations
$99 x+101 y =499 $
$101 x+99 y =501$
$--------$
$200 x+200 y =1000$
Dividing both sides by 200
$x+y=5\dots(III)$
Subtract equation (I) and (II)
$\begin{array}{c}99 x+101 y=499 \\-101 x-99 y=-501 \\\hline-2 x+2 y=-2\end{array}$
Divide both sides by ( -2 )
$x-y=1 \ldots( IV )$
Equating Eq. (III) and (IV)
$x+y=5 $
${x-y=1}$
$----$
${2 x=6} $
$x=\frac{6}{2} $
$x=3$
Substituting $x=3$ in Eq. III
$3+y=5 $
$y=5-3$
$y=2$
$\therefore$ solution is $(x, y)=(3,2)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from P-1 Linear Equations in Two Variables→P-1 Linear Equations in Two Variables — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

A river 1.5 m deep and 36m wide is flowing at the rate of 3.5km/hr. Find the amount of water (in cubi metres) that runs into the sea per minute.

Find the slope of the line passing through the points.
(i) $(-1,4)(3,-7)$
(ii) $(5,5),(1,6)$
(iii) $(1,7)(4,8)$
(iv) $(4,8),(5,5)$
(v) $(4,1)(2,-3)$
(vi) $(4,4),(3,5)$

Which of the following are quadratic equations?
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=3\Big(\text{x}+\frac{1}{\text{x}}\Big)+4$

Find k if the line passing through points P(-12,-3) and Q(4, k)has slope $\frac{1}{2}$.

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:
$h(t) = t^2 - 15$

Find the HCF of the following pairs of integers and express it as a linear combination of them.
1288 and 575

A calf is teid with a rope of length $6\ m$ at the corner of a square grassy lawn of side $20\ m$. If the length of the rope is increased by $5.5\ m$, find the increase in area of the grassy lawn in which the calf can graze.

Very-Short and Short-Answer Questions.
Find the value of $\sin48^\circ\sec42^\circ+\cos48^\circ\text{cosec }42^\circ.$

A wire when bent in the form of an equilateral triangle encloses an area of $121\sqrt{3}\text{cm}^2.$ The same wire is bent to form a circle. Find the area enclosed by the circle. $\Big[\text{Use }\pi=\frac{22}{7}\Big]$

Find the nature of the roots of the following quadratic equations:$2x^2 - 8x + 5 = 0$