Question

Solve the following systems of equations:
4x+5y=-4
4x+3y=12

X=?
Y=?

Answer 1

x = 9 and y = -8

Explanation:

It is given that,

4x + 5y = -4 ----(1)

4x + 3y = 12 -----(2)

To find the value of x and y

eq (1) - eq (2) ⇒

4x + 5y = -4 ----(1)

4x + 3y = 12 -----(2)

0 + 2y = -16

y = -16/2 = -8

Substitute the value of y in eq (1)

4x + 5y = -4 ----(1)

4x + 5*-8 = -4

4x - 40 = -4

4x = -4 + 40 = 36

x = 36/4 = 9

x = 9 and y = -8

Answer 2

For this case we have the following system of equations:

`4x + 5y = -4\\4x + 3y = 12`

We multiply the second equation by -1:

`-4x-3y = -12`

We add the equations:

`4x-4x + 5y-3y = -4-12\\5y-3y = -4-12\\2y = -16\\y = \frac {-16} {2}\\y = -8`

We find the value of "x":

`4x = 12-3y\\x = \frac {12-3y} {4}\\x = \frac {12-3 (-8)} {4}\\x = \frac {12 + 24} {4}\\x = \frac {36} {4}\\x = 9`

Thus, the solution of the system is given by:

`(x, y) :( 9, -8)`

ANswer:

(9, -8)