Solve for x and y: 23x - 29y = 98, 29x - 23y = 110 - Vidyadip

Question

Solve for x and y:
23x - 29y = 98,
29x - 23y = 110

✓

Answer

The given equations are: 23x - 29y = 98 ...(i) 29x - 23y = 110 ...(ii) Adding (i) and (ii), we get 52x + 52y = 208 ⇒ x + y = 4 ...(iii) Subtract (i) from (ii), we get 6x - 6y = 12 ⇒ x - y = 2 ...(iv) Adding (iii) and (iv), we get 2x = 6 ⇒ x = 3 Substituting x = 3 in (iii), we get y = 1Hence, x = 3 and y = 1

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 "5 Marks Questions" from Linear Equations In Two Variables→Linear Equations In Two Variables — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

The difference between the sides at right angle in a right-angled triangle is 7cm. The area of the triangle is $60cm^2$. Find its perimeter.

The difference of the squares of two natural numbers is 45. The squares of the smaller number is four times the largest number. Find the numbers.

The following table gives the production yield per hectare of wheat of 100 farms of a village.

Production yield (kg/ha)	50-55	55-60	60-65	65-70	70-75	75-80
Number of farms	2	8	12	24	38	16

Change the distribution to a 'more than type' distribution and draw its ogive. Using ogive, find the median of the given data.

If the ratio of the sum of the first $n$ terms of two A.Ps is $(7 n+1):(4 n+27)$, then find the ratio of their $9^{\text {th }}$terms.

If the median of the following frequency distribution is 28.5 find the missing frequencies:

Class interval	0-10	10-20	20-30	30-40	40-50	50-60	Total
Frequency	5	$f_1$	20	15	$f_2$	5	60

Divide 29 into two parts so that the sum of the squares of the parts is 425.

Solve the following quadratic equations by factorization:
$\frac{4}{\text{x}}-3=\frac{5}{2\text{x}+3},$ $\text{x}\neq-0,-\frac{3}{2}$

If $\tan\theta=\frac{20}{21},$ show that $\frac{\big(1-\sin\theta+\cos\theta\big)}{\big(1+\sin\theta+\cos\theta\big)}=\frac37.$

Find the sum of first 100 even natural numbers which are divisible by 5.

The angle of elevation of the top of a tower 30m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower.