Question

Solve the system by elimination

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2x + 5y = −24

3x − 5y = 14

Answer 1

Answer: x = - 2, y = - 4

Explanation:

The given system of equations is expressed as

2x + 5y = −24- - - - - - - - - - - - 1

3x − 5y = 14- - - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 2. It becomes

6x + 15y = - 72

6x - 10y = 28

Subtracting, it becomes

15y - - 10y = - 72 - - 28

25y = - 100

Dividing the left hand side and the right hand side of the equation by 25, it becomes

25y/25 = - 100/25

y = - 4

Substituting y = - 4 into equation 1, it becomes

2x + 5 × - 4= −24

2x - 20 = 24

2x = - 24 + 20 = - 4

x = - 4/2 = - 2

Answer 2

The answer to your question is x = -22; y = 4

Explanation:

System of equations

2x + 5y = -24 ------------- l

3x - 5y = 14 ------------- ll

Process

1.- Multiply equation l equation l by 3 and equation ll by -2

6x + 15y = -72

-6x + 10y = -28 Add the equations

0 + 25y = 100

2.- Solve for y

y = 100/25

y = 4

3.- Substitute y in equation l to find x

2x + 5(4) = -24

Solve for x

2x + 20 = -24

2x = -24 - 20

2x = -44

x = -44/2

x = -22