Question

- Determine which point is a solution to the following system of equations: x + y = -4 -2x - 2y = 6 a) (-5,1) b) (0, -3) c) There are infinite solutions. d) There is no solution.

Answer 1

there is no solution (option D)

Step-by-step explanation:

x + y = -4 ...equation 1

-2x - 2y = 6 ...equation 2

using elimination method:

let's eliminate y. Multiply equation 1 by 2 so the coefficient of y are the same:

2x + 2y = -8 ...equation 1

-2x - 2y = 6 ...equation 2

Add equation 1 and 2:

2x + (-2x) + 2y + (- 2y) = -8 + 6

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

2x - 2x + 2y - 2y = -2

0 + 0 = -2

0 = -2

left side not equal to right side of the equation

When the left hand side of the equation has a different number from the right hand side of the equation, we say there is no solution (option D)