Question

Which ordered pair is a solution to the system of linear equations?

2x + 3y= 6

–3x + 5y = 10

(0,2)
(2,0)
(3,2)
(2,3)

Answer 1

Answer: Option (A) (0, 2) is the correct.

Step-by-step explanation: We are given to select the correct ordered pair that is a solution to the following system of linear equations :

`2x+3y=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-3x+5y=10~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

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

`6x+9y=18~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)\\\\-6x+10y=20~~~~~~~~~~~~~~~~~~~~~~~~(iv)`

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

`9y+10y=18+20\\\\\Rightarrow 19y=38\\\\\Rightarrow y=(38)/(19)\\\\\Rightarrow y=2.`

Substituting the value of y in equation (ii), we get

`-3x+5*2=10\\\\\Rightarrow -3x+10=10\\\\\Rightarrow -3x=0\\\\\Rightarrow x=0.`

Thus, the required ordered pair solution is (0, 2).

Option (A) is CORRECT.

Answer 2

2x + 3y = 6 multiplied by 3
-3x + 5y = 10 multiplied by 2

6x + 9y = 18
-6x + 10y = 20
19y = 38
y = 38 / 19
y = 2

2x + 3x2 = 6
2x + 6 = 6
2x = 0
x = 0/2
x = 0

The correct answer is (0,2)