Question

Solve the following system of equations 3x - 2y =5 -2x - 3y = 14

Answer 1

Answer:

The solution is:

$(-1, -4)$

Step-by-step explanation:

We have the following equations

$3x - 2y =5$

$-2x - 3y = 14$

To solve the system multiply by $\frac{3}{2}$ the second equation and add it to the first equation

$-2*\frac{3}{2}x - 3\frac{3}{2}y = 14\frac{3}{2}$

$-3x - \frac{9}{2}y = 21$

$3x - 2y =5$

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

$-\frac{13}{2}y=26$

$y=-26*\frac{2}{13}$

$y=-4$

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

Answer:

x = -1 and y = -4

Step-by-step 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