Solve for x and y: 2x+5y=8 3 , 3x-2y=5 6 - Vidyadip

Question

Solve for x and y:
$\text{2x}+\text{5y}=\frac{8}{3},$
$3\text{x}-\text{2y}=\frac{5}{6}$

✓

Answer

The given equations are: $\text{2x}+\text{5y}=\frac{8}{3}\ \dots(1)$ $\text{3x}-\text{2y}=\frac{5}{6}\ \dots(2)$ Multiply (1) by 2 and (2) by 5 $\text{4x}+\text{10y}=\frac{16}{3}\ \dots(3)$ $\text{15x}-\text{10y}=\frac{25}{6}\ \dots(4)$Adding (3) from (4), we get
$19\text{x}=\frac{57}6{}$ $\Rightarrow\text{x}=\frac{57}{6\times19}=\frac{1}{2}$Substitution $\text{x}=\frac{1}{2}$ in (3), we get
$2\times\frac{1}{2}+\text{10y}=\frac{16}{3}$ $\text{10y}=\frac{16}{3}-2$ $\Rightarrow\text{10y}=\frac{10}{3}$ $\text{y}=\frac{10}{3\times10}=\frac{1}{3}$$\therefore$ Solution is $\text{x}=\frac{1}{2}$ and $\text{y}=\frac{1}{3}$

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 "3 Marks Question" from Linear Equation In Two Variable→Linear Equation In Two Variable — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Write any two linear equations in two variables in which the value of one variable is 12 and the other 10

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is $104\ cm$ and the radius of each of the hemispherical ends is $7\ cm$, find the cost of polishing its surface at the rate of $Rs\ 10\ per\ dm^2.$

How many numbers of two digit are divisible by $3$?

Very-short and Short-Answer Questions.
Write the value of $\sin\theta\cos(90^\circ-\theta)+\cos\theta\sin(90^\circ-\theta).$

A dealer has given 10% discount on a showpiece of Rs. 25,000. GST of 28% was charged on the discounted price. Find the total amount shown in the tax invoice. What is the amount of CGST and SGST?

Find the zeros of the polynomial $x^2 + 2x - 195$

Two types of boxes A, B are to be placed in a truck having capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.

Solve for x and y:
0.3x + 0.5y = 0.5,
0.5x + 0.7y = 0.74

Mukund possesses ₹50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.

The line segment AB is divided into five congruent parts at P, Q, R and S suchthat A-P-Q-R-S-B. If point Q(12, 14) and
S(4, 18) are given find thecoordinates of A, P, R,B.