Question

solve the simultaneous linear equation

Answer 1

Answer:

x = 5 and y =-2

Step-by-step explanation:

2x+3y = 4

3x+2y = 11

Multiply first equation by 2 throughout and second equation by 3 we get

4x + 6y = 8

9x + 6y = 33

subtracting the equations we get

9x - 4x = 33-8

5x =  25

x = 5

substituting x= 5 in 1st equation

10 + 3y = 4

3y = 4-10

3y = -6

y = -6/3

y= -2

Answer 2

Required Solution :

For first equation,

• 2x + 3y = 4

$: \longmapsto \: \sf{2x \: = \: 4 - 3y}$

$: \longmapsto \: \boxed{\sf{x \: = \: \dfrac{4 \: - \: 3y}{2}}}$

Now, substitute this value of x in second equation.

$: \longmapsto \: \sf{3 \bigg( \dfrac{4 - 3y}{2} \bigg) + 2y \: = \: 11}$

$: \longmapsto \: \sf{3 \times \bigg( \dfrac{4 - 3y}{2} \bigg) + 2y \: = \: 11}$

$: \longmapsto \: \sf{ \dfrac{12 \: - \: 9y }{2} + 2y \: = \: 11}$

$: \longmapsto \: \sf{ \dfrac{12 \: - \: 9y \: + 4y }{2} \: = \: 11}$

$: \longmapsto \: \sf{ \dfrac{12 \: - \: 5y }{2} \: = \: 11}$

$: \longmapsto \: \sf{ 12 \: - \: 5y \: = \: 11 \times2}$

$: \longmapsto \: \sf{ 12 \: - \: 5y \: = \: 22}$

$: \longmapsto \: \sf{ - \: 5y \: = \: 22 \: - \: 12}$

$: \longmapsto \: \sf{ - \: 5y \: = \:10}$

$: \longmapsto \: \sf{ y \: = \: - \dfrac{10}{5} }$

$: \longmapsto \: \red{ \boxed{\bf{ y \: = \: - 2 }}}$

Finding out value of x :

$: \longmapsto \: \sf{x \: = \: \dfrac{4 - 3( - 2)}{2} }$

$: \longmapsto \: \sf{x \: = \: \dfrac{4 - 3 \times ( - 2)}{2} }$

$: \longmapsto \: \sf{x \: = \: \dfrac{4 + 6}{2} }$

$: \longmapsto \: \sf{x \: = \: \dfrac{10}{2} }$

$: \longmapsto \: \sf{x \: = \: \cancel\dfrac{10}{2} }$

$: \longmapsto \: \red{ \boxed{\bf{ x \: = \: 5 }}}$