Question

Solve the following system of equations

-4x - 9y =24

7x + 3y =9

Answer 1

x = 3 and y = -4

Explanation:

It is given that,

-4x - 9y = 24 -----(1)

7x + 3y = 9 ---(2)

To find the solution of given equations

eq(2) * 3 ⇒

21x + 9y = 27 -----(3)

eq(1) + eq(3) ⇒

-4x - 9y = 24 -----(1)

21x + 9y = 27 -----(3)

17x = 51

x = 51/17 = 3

Substitute the value of x in eq(1)

-4x - 9y = 24 -----(1)

-4*3 - 9y = 24

-9y = 24 + 12

-9y = 36

y = 36/(-9) = -4

Therefore x = 3 and y = -4

Answer 2

The solution is:

`(3, -4)`

Explanation:

We have the following equations

`-4x - 9y =24`

`7x + 3y =9`

To solve the system multiply by 3 the second equation and add it to the first equation

`3*7x + 3*3y =3*9`

`21x + 9y =27`

`-4x - 9y =24`

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`17x=51`

`x=(51)/(17)`

`x=3`

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

`7(3) + 3y =9`

`21 + 3y =9`

`3y =9-21`

`3y =-12`

`y =-(12)/(3)`

`y =-4`

The solution is:

`(3, -4)`