Question

if x+y=7 and x+2y=9 then the value of y

Answer 1

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Answer 2

Given:

x+y=7 and x+2y=9

To Find:

The value of y

Solution:

If we are given two sets of linear equations with two variables then we can find the solution using the elimination method in which we multiply any of the equations with some number to equal the coefficient of any of the two variables and then subtract them together to find the solution, here we will solve by first equalizing the x variable then the y variable,

Using x variable,

$x+y=7$      -(1)

$x+2y=9$     -(2)

as we can see that the x variable already has an equal coefficient so, we will subtract equation 1 with equation 2

$x+2y-x-y=9-7\\y=2$

So the value comes as 2.

Using y variable,

$x+y=7$     -(1)

$x+2y=9$    -(2)

as we can see that the coefficients are not equal so multiply equation 1 with 2 and subtract equation 1 with 2, we get,

$2(x+y)-x-2y=14-9\\2x+2y-x-2y=5\\x=5$

Now substituting the value of x in equation 1, we have,

$x+y=7\\5+y=7\\y=2$

So the value comes as 2.

Hence, the value of y is 2.