Question

5. Solve the system of linear equations. 2x + 6y = -3 2x + y = 0 A. (0, 2) B. (9,7) C. no solution D. infinitely many solutions licorutions

Answer 1

EXPLANATION

Given the system of equations:

(1) 2x + 6y = -3

(2) 2x + 6y = 0

Subtract 6y from both sides:

2x + 6y - 6y = -3 - 6y

Simplify:

2x = -3 - 6y

Divide both sides by 2:

`(2x)/(2)=-(3)/(2)-(6y)/(2)`

Simplify:

`x=(-3-6y)/(2)`

Substitute:

`x=(-3-6y)/(2)`
`2\cdot(-3-6y)/(2)+6y\text{ = 0}`

Simplifying:

`-3-6y+6y=0`

Adding like terms:

`-3=0`

-3=0 is false, therefore the system of equations has no solutions.

The answer is the option C.