Match the systems of linear equations with their solutions.

Step-by-step explanation:

A). Linear equation are x + y = -1 ----------(1)

and -6x + 2y = 14 ------(2)

First we multiply equation 1 by 6 then we add it to equation 2.

6(x + y) + (-6x + 2y) = -6 + 14

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

8y = 8

y = 1

By putting y = 1 in the equation 1

1 + x = -1

x = -1 -1 = -2

Solution will be (-2, 1)

B). Linear equations are x - 2y = -5 -----(1)

and 5x + 3y = 27 ------(2)

We multiply equation 1 by 5 and subtract it from 2

(5x + 3y) - 5(x - 2y) = 27 - 5(-5)

5x + 3y - 5x + 10y = 27 + 25

13y = 52

y = 4

By putting y = 4 in equation 1

x = -5 + 2y = -5 + 2(4)

  = -5 + 8

  = 3

solutions will be (3, 4)

C). -4x + y = -9 -----(1)

5x + 2y = 3 ----(2)

We multiply equation 1 by 2 and subtract it from equation 2

5x + 2y - 2(-4x + y) = 3 - 2(-9)

5x + 2y + 8x - 2y = 3 + 18

13x = 21

x =

By putting x = in equation 1

y = 9 + 4y

 = 9 + 4()

 = 9 +

 =

Solution will be

D). 6x + 3y = -6 ---- (1)

    2x + y = -2 ------(2)

By multiplying equation 2 by (-3) and add it to equation 1

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

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

0 = 0

Therefore, this equation has infinite solutions.

E). -x + 2y = 4 ----(1)

    -3x + 6y = 11

   3(-x + 2y) = 11

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

So this system of linear equations has no solution.

F). -7x + y = 1 ---- (1)

  14x - 7y = 28 -----(2)

We divide equation 2 by 7 and add it to the equation 1

-7x + y + 2x -y = 1 + 4

-5x = 5

x = -1

Now we put x = -1 in equation 1

-7(-1) + y = 1

7 + y = 1

y = 1 - 7

y = -6

So the solution will be (-1, -6)

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