Question

Solve the following system of equations

3x - 2y =55

-2x - 3y = 14

Answer 1

x = 411/39 and y = -152/13

Explanation:

It is given that,

3x - 2y = 55 ----(1)

-2x - 3y = 14 ---(2)

To find the solution of given equations

eq(1) * 2 ⇒

6x - 4y = 110 ---(3)

eq(2) * 3 ⇒

-6x - 9y = 42 ---(4)

eq(3) + eq(4) ⇒

6x - 4y = 110 ---(3)

-6x - 9y = 42 ---(4)

0 - 13y = 152

y = -152/13

Substitute the value of y in eq (1)

3x - 2y = 55 ----(1)

3x - 2*(-152/13) = 55

3x + 304/13 = 55

3x = 411/13

x = 411/39

Therefore x = 411/39 and y = -152/13

Answer 2

The solution is:

`((137)/(13), -(152)/(13))`

Explanation:

We have the following equations

`3x - 2y =55`

`-2x - 3y = 14`

To solve the system multiply by
`(3)/(2)` the second equation and add it to the first equation

`-2*(3)/(2)x - 3(3)/(2)y = 14(3)/(2)`

`-3x - (9)/(2)y = 21`

`3x - 2y =55`

---------------------------------------

`-(13)/(2)y=76`

`y=-76*(2)/(13)`

`y=-(152)/(13)`

Now substitute the value of y in any of the two equations and solve for x

`-2x - 3(-(152)/(13)) = 14`

`-2x +(456)/(13) = 14`

`-2x= 14-(456)/(13)`

`-2x=-(274)/(13)`

`x=(137)/(13)`

The solution is:

`((137)/(13), -(152)/(13))`