Question

Solve the following system of equations

3x - 2y =5

-2x - 3y = 14

Answer 1

The solution is:

`(-1, -4)`

Explanation:

We have the following equations

`3x - 2y =5`

`-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 =5`

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`-(13)/(2)y=26`

`y=-26*(2)/(13)`

`y=-4`

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

`-2x - 3(-4) = 14`

`-2x +12 = 14`

`-2x= 14-12`

`-2x=2`

`x=-1`

The solution is:

`(-1, -4)`

Answer 2

x = -1 and y = -4

Explanation:

It is given that,

3x - 2y = 5 ----(1)

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

To find the solution of equations

(1) * 2 ⇒

6x - 4y = 10 -----(3)

(2) * 3 ⇒

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

eq(3) + eq(4) ⇒

6x - 4y = 10 -----(3)

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

0 - 13y = 52

y = 52/(-13) = -4

Substitute the value of y in eq(1)

3x - 2y = 5 ----(1)

3x - (2 * -4) = 5

3x +8 = 5

3x = 5 - 8 = -3

x = -3/3 = -1

Therefore x = -1 and y = -4