Question

2x+5y=7, 3x-2y=-18 find the valye of x and y by elemination method ​ please do it fast

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of linear equations are

$\rm \: 2x + 5y = 7 - - - (1)$

and

$\rm \: 3x - 2y = - 18 - - - (2)$

On multiply equation (1) by 3, we get

$\rm \: 6x + 15y = 21 - - - (3)$

On multiply equation (2) by 2, we get

$\rm \: 6x - 4y = - 36 - - - (4)$

On Subtracting equation (4) from equation (3), we get

$\rm \:19y = 57$

$\rm\implies \:\boxed{\tt{ y \: = \: 3 \: }}$

On substituting y = 3, in equation (1), we get

$\rm \: 2x + 5(3)= 7$

$\rm \: 2x + 15= 7$

$\rm \: 2x = 7 - 15$

$\rm \: 2x = - 8$

$\rm\implies \:\boxed{\tt{ \: x \: = \: - \: 4 \: }}$

Hence, Solution set of pair of equation is given by

$\red{\begin{gathered}\begin{gathered}\bf\: \begin{cases} &\sf{x \: = \: - \: 4 \: } \\ \\ &\sf{y \: = \: 3} \end{cases}\end{gathered}\end{gathered}}$

VERIFICATION

Consider

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

On substituting the values of x and y, we get

$\rm \: 2( - 4) + 5(3) = 7$

$\rm \: - 8+ 15 = 7$

$\rm\implies \:7 = 7$

Hence, Verified

Now, Consider

$\rm \: 3x - 2y = - 18$

On substituting the values of x and y, we get

$\rm \: 3( - 4) - 2(3) = - 18$

$\rm \: - 12 - 6 = - 18$

$\rm\implies \: - 18 = - 18$

Hence, Verified

Answer 2

Answer:

- + -

___________

5y = -6

y=−

5

−6

3x−2(−

5

6

)=24

=3x+

5

12

=24

=3x=24−

5

12

=

5

120−12

=

5

108

∴x=

5

36

x+y=

5

36−6

=

5

30

=6

x−y=

5

36+6

=

5

42