The solution of the equation \( x-y=10 \) and \( x+y=70 \) is \( \ldots \)
A) \( (40,30) \)
B) (30,40)
C) \( (10,60) \)
D) \( (50,20) \)
Given:
The given pair of equations is \( x-y=10 \) and \( x+y=70 \).
To do:
We have to find the solution of the given system of equations.
Solution:
Adding the given equations, we get,
$(x-y)+(x+y)=10+70$
$x+x-y+y=80$
$2x=80$
$x=\frac{80}{2}$
$x=40$
Substituting $x=40$ in $x+y=70$, we get,
$40+y=70$
$y=70-40$
$y=30$
Therefore, the solution of the given system of equations is $(40, 30)$.
Related Articles
- One equation of a pair of dependent linear equations is \( -5 x+7 y=2 \). The second equation can be(A) \( 10 x+14 y+4=0 \)(B) \( -10 x-14 y+4=0 \)(C) \( -10 x+14 y+4=0 \),b>(D) \( 10 x-14 y=-4 \)
- If $x=a,\ y=b$ is the solution of the pair of equations $x-y=2$ and $x+y=4$, find the value of $a$ and $b$.
- A pair of linear equations which has a unique solution \( x=2, y=-3 \) is(A) \( x+y=-1 \)\( 2 x-3 y=-5 \)(B) \( 2 x+5 y=-11 \)\( 4 x+10 y=-22 \)(C) \( 2 x-y=1 \)\( 3 x+2 y=0 \)(D) \( x-4 y-14=0 \)\( 5 x-y-13=0 \)
- Find the value of \( k \), if \( x=2, y=1 \) is a solution of the equation \( 2 x+3 y=k \)
- If \( x=a, y=b \) is the solution of the equations \( x-y=2 \) and \( x+y=4 \), then the values of \( a \) and \( b \) are, respectively(A) 3 and 5(B) 5 and 3(C) 3 and 1,b>(D) \( -1 \) and \( -3 \)
- Find the sum of the following arithmetic progressions:\( \frac{x-y}{x+y}, \frac{3 x-2 y}{x+y}, \frac{5 x-3 y}{x+y}, \ldots \) to \( n \) terms
- 1. Factorize the expression \( 3 x y - 2 + 3 y - 2 x \)A) \( (x+1),(3 y-2) \)B) \( (x+1),(3 y+2) \)C) \( (x-1),(3 y-2) \)D) \( (x-1),(3 y+2) \)2. Factorize the expression \( \mathrm{xy}-\mathrm{x}-\mathrm{y}+1 \)A) \( (x-1),(y+1) \)B) \( (x+1),(y-1) \)C) \( (x-1),(y-1) \)D) \( (x+1),(y+1) \)
- The angles of a cyclic quadrilateral \( A B C D \) are\( \angle \mathrm{A}=(6 x+10)^{\circ}, \angle \mathrm{B}=(5 x)^{\circ}, \angle \mathrm{C}=(x+y)^{\circ}, \angle \mathrm{D}=(3 y-10)^{\circ} \)Find \( x \) and \( y \), and hence the values of the four angles.
- Factorize the algebraic expression $a^2(x+y)+b^2(x+y)+c^2(x+y)$.
- Solve the following pairs of linear equations: (i) \( p x+q y=p-q \)$q x-p y=p+q$(ii) \( a x+b y=c \)$b x+a y=1+c$,b>(iii) \( \frac{x}{a}-\frac{y}{b}=0 \)$a x+b y=a^{2}+b^{2}$(iv) \( (a-b) x+(a+b) y=a^{2}-2 a b-b^{2} \)$(a+b)(x+y)=a^{2}+b^{2}$(v) \( 152 x-378 y=-74 \)$-378 x+152 y=-604$.
- Solve the following pairs of equations:\( \frac{2 x y}{x+y}=\frac{3}{2} \)\( \frac{x y}{2 x-y}=\frac{-3}{10}, x+y ≠ 0,2 x-y ≠ 0 \)
- Subtract $24 x y-10 y-18 x$ from $30 x y +12 y+14 x$
- Factorize the algebraic expression $a(x-y)+2b(y-x)+c(x-y)^2$.
- If $x=34$ and $y=x$, what is the value of $x+y$?
- Find the sum of the following arithmetic progressions:\( (x-y)^{2},\left(x^{2}+y^{2}\right),(x+y)^{2}, \ldots, \) to \( n \) terms
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies