Question

Solve the system of equation below.

5x+2y=9
2x-3y=15

A.(3,-3)
B.(12,-3)
C.(-3,12)
D.(-3,3)

Answer 1

Answer: The correct option is (A) (3, -3).

Step-by-step explanation: We are given to solve the following system of equations :

`5x+2y=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-3y=15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

We will be using the method of ELIMINATION to solve the given system.

Multiplying equation (i) by 3 and equation (ii) by 2, we have

`3(5x+2y)=3*9\\\\\Rightarrow 15x+6y=27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

and

`2(2x-3y)=2*15\\\\\Rightarrow 4x-6y=30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)`

Adding equations (iii) and (iv), we get

`15x+4x=27+30\\\\\Rightarrow 19x=57\\\\\Rightarrow x=(57)/(19)\\\\\Rightarrow x=3`

And from equation (i), we get

`5*3+2y=9\\\\\Rightarrow 15+2y=9\\\\\Rightarrow 2y=-6\\\\\Rightarrow y=-(6)/(2)\\\\\Rightarrow y=-3.`

Thus, the required solution is (x, y) = (3, -3).

Option (A) is CORRECT.

Answer 2

We have the following system of equations:
5x + 2y = 9
2x-3y = 15
Resolving graphically we can obtain the following result:
x = 3
y = -3
Therefore, the ordered pair solution is:
(x, y) = (3, -3)
Answer:
A. (3, -3)