2. If 3x + 5y = 9 and 5x + 3y = 7, then find the value of x + y.
Answers
Answer:
These is a problem of linear equations.
The problems of can be solved by two different methods…
Elemination
Substitution
Here we will discuss about the elemination techniques.
As the name suggest that we need to eleminate the variables (either x or y) to get the answer. Let's understand with the help of an example.
Given eqn
3x+5y=9
5x+3y=7
In order to eleminate “x” we need to make the co-efficient of “x” same on both the equation.
To achieve this
we will multiply 5 with equation 1
And multiply 3 with equation 2
On multiplication it will look like….
15x+25y=45
15x+9y=21
Now we will substract equation 1 and 2, it will give,
16y=24
y=1.5
Now, we will put y = 1.5 in equation 1 and solve
Upon solving we get,
x=0.5
Now, we got both x and y.
So, x+y=0.5+1.5=2
x=1 and y=2/3
Step-by-step explanation:
3x+5y=9_________ eqn-1
5x+3y=7_________ eqn-2
eqn-1 x5 => 15x+25y=45________ eqn-3
eqn-2 x3=> 15x+9y=21__________eqn-4
subtracting eqn-4 from eqn-3
15x+25y=45
-15x-9y= -21
__________________
0x + 16y= 24
=> 16y= 24
=> y=16/24 => 2/3
substitute y=2/3 in in eqn 2
5x+ 3(2/3) = 7
5x+ 2=7
5x= 7-2
5x=5
x=5/5
=>x=1