Question
Solve for x and y:
$\frac{\text{x}}{2}-\frac{\text{y}}2{}=6,$
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5$
$\frac{\text{x}}{2}-\frac{\text{y}}2{}=6,$
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5$
✓
Answer
$\frac{\text{x}}{2}-\frac{\text{y}}2{}=6\ \dots(\text{i})$
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5\ \dots(\text{ii})$
Multiply (ii) by $\frac{1}{3}$ and add it to (i).
$\frac{\text{x}}{21}+\frac{\text{y}}9{}=\frac{5}{3}$ and $\frac{\text{x}}{2}-\frac{\text{y}}{9}=6$
$\Rightarrow\frac{\text{x}}{21}+\frac{\text{x}}{2}=\frac{5}{3}+6$
$\Rightarrow\frac{23\text{x}}{42}=\frac{23}{3}$
$\Rightarrow\text{x}=14$
Substituting x = 14 in (ii), we get y = 9
So, x = 14 and y = 9
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5\ \dots(\text{ii})$
Multiply (ii) by $\frac{1}{3}$ and add it to (i).
$\frac{\text{x}}{21}+\frac{\text{y}}9{}=\frac{5}{3}$ and $\frac{\text{x}}{2}-\frac{\text{y}}{9}=6$
$\Rightarrow\frac{\text{x}}{21}+\frac{\text{x}}{2}=\frac{5}{3}+6$
$\Rightarrow\frac{23\text{x}}{42}=\frac{23}{3}$
$\Rightarrow\text{x}=14$
Substituting x = 14 in (ii), we get y = 9
So, x = 14 and y = 9
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance traveled by the balloon during the interval.
In fig. AE is the bisector of the exterior $\angle\text{CAD}$ meeting BC produced in E. If AB = 10cm, AC = 6cm and BC = 12cm, find CE.
→The following table gives the number of pages written by Sarika for completing her own book for 30 days:
Find the mean number of pages written per day.
|
Number of pages written per day
|
6-18
|
19-21
|
22-24
|
25-27
|
28-30
|
|
Number of days
|
1
|
3
|
4
|
9
|
13
|
The marks distribution of $30$ students in a mathematics examination. Find the mode of this data. Also, compare and interpret the mode and the mean.
→| Class interval | Number of students $(f_i)$ | Classmark $(x_i)$ | $f_ix_i$ |
| 10 - 25 | 2 | 17.5 | 35.0 |
| 25 - 40 | 3 | 32.5 | 97.5 |
| 40 - 55 | 7 | 47.5 | 332.5 |
| 55 - 70 | 6 | 62.5 | 375.0 |
| 70 - 85 | 6 | 77.5 | 465.0 |
| 85 - 100 | 6 | 92.5 | 555.0 |
| Total | $\sum f_{i}$ = 30 | $\sum f_{i}x_i$ = 1860.0 |
Very-Short and Short-Answer Questions.If $\text{cosec }\theta=2\text{x}$ and $\cot\theta=\frac{2}{\text{x}},$ find the value of $2\Big(\text{x}^2-\frac{1}{\text{x}^2}\Big).$
→Find the area of a sector of a circle with radius 6 cm, if the angle of the sector is $60^o.$
→In a $\triangle\text{ABC,D}\ \text{and E}$ are points on the sides AB and AC respectively such that DE || BC.
If AD = 2cm, AB = 6cm and AC = 9cm, find AE.
→If AD = 2cm, AB = 6cm and AC = 9cm, find AE.
The surface area of a solid metallic sphere is $616cm^2$. It is melted and recast into a cone of height 28cm. Find the diameter of the base of the cone so formed $(\text{use}\pi=\frac{22}{7}).$
→For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.
$\frac{-3}{2\sqrt{5}},-\frac{1}{2}$
→$\frac{-3}{2\sqrt{5}},-\frac{1}{2}$
Find:
$11^{th}$ term of the $A.P. 10.0, 10.5, 11.0, 11.5, .....$
→$11^{th}$ term of the $A.P. 10.0, 10.5, 11.0, 11.5, .....$