Question

Solve using the method of substitution
$2x-3y=7;5x+y=9$

Answer 1

Hint: Here we have been given two equations and we have to solve them using a substituting method. Firstly we will take one equation and get the value of one variable from it. Then we will substitute the value of the variable obtained in another equation and simplify it to get the value of one unknown variable. Finally put that value in the back in any of the equations and get the value of another unknown variable and our desired answer.

Complete step by step answer:
The two equations are given as follows,
$2x-3y=7$…..$\left( 1 \right)$
$5x+y=9$…..$\left( 2 \right)$
As we can see that value of variable $y$ can easily be determined by equation (2) so on solving equation (2) we get,
$\Rightarrow y=9-5x$
Substitute the above value in equation (1) as follows,
$\Rightarrow 2x-3\left( 9-5x \right)=7$
$\Rightarrow 2x-27+15x=7$
On taking the variable on one side and the constant on another we get,
$\Rightarrow 2x+15x=7+27$
$\Rightarrow 17x=34$
Simplifying further we get,
$\Rightarrow x=\dfrac{34}{17}$
$\Rightarrow x=2$
On substituting the above value in equation (1) we get,
$\Rightarrow 2\times 2-3y=7$
$\Rightarrow 4-3y=7$
Taking constant on right side we get,
$\Rightarrow -3y=7-4$
$\Rightarrow -3y=3$
So we get,
$\Rightarrow y=\dfrac{3}{-3}$
$\Rightarrow y=-1$
So we got the value as $x=2$ and $y=-1$ .
Hence on solving equation $2x-3y=7;5x+y=9$ we get the solution as $x=2$ and $y=-1$ .

Note:
 If we are given two linear equations then we can solve them in many ways like using elimination method, substitution method and matrix method.
We can solve this question using the elimination method. In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.