Solve for x and y: 5 x +6y=13, 3 x +4y=7 (x 0). - Vidyadip

Question

Solve for x and y:
$\frac{5}{\text{x}}+\text{6y}=13,$
$\frac{3}{\text{x}}+\text{4y}=7\ (\text{x}\neq0).$

✓

Answer

Putting $\frac{1}{\text{x}}=\text{u}$ the given equations become 5u + 6y = 13 ...(1) 3u + 4y = 7 ...(2)Multiplying (1) by 4 and (2) by 6, we get
20u + 24y = 52 ...(3)
18u + 24y = 42 ...(4)
Subtracting (4) from (3), we get
2u = 10
⇒ x = 5
Substituting u = 5 in (1), we get
5 × 5 + 6y = 13
⇒ 6y = 13 - 25
⇒ 6y = -12
⇒ y = -2
u = 5
$\Rightarrow\frac{1}{\text{x}}=5$ $\Rightarrow\text{5x}=1$ $\Rightarrow\text{x}=\frac{1}{5}$$\therefore$ The solution is $\text{x}=\frac{1}{5}$ and y = -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 "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

Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to $\frac{\big(\text{a+c}\big)\big(\text{b + c - 2a}\big)}{2\big(\text{b - a}\big)}.$

If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.

The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below:

Mileage (km/ l)	10-12	12-14	14-16	16-18
Number of cars	7	12	18	13

Find the mean mileage.
The manufacturer claimed that the mileage of the model was 16km/ litre. Do you agree with this claim?

Solve the following quadratic equation:
$\Big(\frac{\text{x}}{\text{x}}+1\Big)^2-5\Big(\frac{\text{x}}{\text{x}+1}\Big)+6=0,$ $\text{x}\neq-1$

A bucket of height 24cm is in the form of frustum of a cone whose circular ends are of diameter 28cm and 42cm. Find the cost of milk at the rate of ₹ 30 per litre, which the bucket can hold.

Prove that the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

Find the roots of the following quadratic equation (if they exist) by the method of completing the square.
$\text{x}^2-4\sqrt{2\text{x}}+6=0$

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis:
2x - 3y + 6 = 0, 2x + 3y - 18 = 0

Find the value of k for which each of the following system of equations have infinitely many solutions:

$(k + 2)x - (2k + 1)y = 3(2k - 1)$

The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are $30^{\circ}$ and $60^{\circ}$ respectively. Find the difference between the heights of the building and the tower and the distance between them.