Question
Solve for x and y:
$\text{x}-\text{y}=3$
$\frac{\text{x}}{3}+\frac{\text{y}}{2}=6$
$\text{x}-\text{y}=3$
$\frac{\text{x}}{3}+\frac{\text{y}}{2}=6$
✓
Answer
The given equation are:
$\text{x}-\text{y}=3\dots(\text{i})$
$\frac{\text{x}}{3}+\frac{\text{y}}{2}=6\dots(\text{ii})$
Multiply (i) by $\frac{1}2{}$ and add it to (ii).
$\frac{\text{x}}{2}-\frac{\text{y}}{2}=\frac{3}{2}$ and $\frac{\text{x}}{3}+\frac{\text{y}}{2}=6$
$\Rightarrow\frac{\text{x}}2{}+\frac{\text{x}}{3} =\frac{3}{2}+6$
$\Rightarrow\frac{\text{5x}}6{}=\frac{15}2{}$
$\Rightarrow\text{x}=9$
Substituting in (i), we get y = 6
So, x = 9 and y = 6
$\text{x}-\text{y}=3\dots(\text{i})$
$\frac{\text{x}}{3}+\frac{\text{y}}{2}=6\dots(\text{ii})$
Multiply (i) by $\frac{1}2{}$ and add it to (ii).
$\frac{\text{x}}{2}-\frac{\text{y}}{2}=\frac{3}{2}$ and $\frac{\text{x}}{3}+\frac{\text{y}}{2}=6$
$\Rightarrow\frac{\text{x}}2{}+\frac{\text{x}}{3} =\frac{3}{2}+6$
$\Rightarrow\frac{\text{5x}}6{}=\frac{15}2{}$
$\Rightarrow\text{x}=9$
Substituting in (i), we get y = 6
So, x = 9 and y = 6
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
If $\sec \theta=\frac{41}{40}$, then find values of $\sin \theta, \cot \theta, \operatorname{cosec} \theta$
→For what value of $\alpha,$ the system of equations will have no solution
$\alpha\text{x}+3\text{y}=\alpha-3$
$12\text{x}+\alpha\text{y}=\alpha$
→$\alpha\text{x}+3\text{y}=\alpha-3$
$12\text{x}+\alpha\text{y}=\alpha$
In adjoining figure, AP ⊥ BC, AD || BC, then find A(ΔABC) : A (ΔBCD)
Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9cm.
$500$ persons have to dip in a rectangular tank which is $80m$ long and $50m$ broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is $0.04m^3$?
→For what value of k does the system of equations:
$x + 2y = 5, 3x + ky + 15 = 0$
have;
→$x + 2y = 5, 3x + ky + 15 = 0$
have;
- A unique solution,
- No solution?
A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius. The total height of the toy is 15.5cm. Find the total surface area of the toy.
The length of three concesutive sides of a quadilateral circumscribing a circle are 4cm, 5cm, 7cm respectively. Determine the length of thefourth side.
The first term of an A.P. is p and its common difference is q. Find its $10^{th}$ term.
→Two buildings are facing each other on a road of width 12 metre. From the top of the first building, which is 10 metre high, the angle of elevation of the top of the second is found to be 60°. What is the height of the second building?