Question

A student solved a system of equations by elimination. Describe and correct the error made in the part of the solution shown.

Answer 1

Answer:

x = -2; y = 3

Step-by-step explanation:

5x + 4y = 2 (1)

3x + 3y = 3 (2)

Multiply (1) by 3 and (2) by 4

15x + 12y = 6 (3)

12x + 12y = 12 (4)

Subtract (4) from (3)

15x - 12x = 6 - 12

3x = -6

x = -6/3

x = -2

Substitute x = -2 into (1)

5x + 4y = 2

5(-2) + 4y = 2

-10 + 4y = 2

4y = 2 +10

4y = 12

y = 12/4

y = 3

The first error is when he multiplied equation (2) by 4

He didn't multiply the right hand side of the equation by 4

3x + 3y = 3 ×4

12x + 12y = 12

But he wrote

12x + 12y = 3

The the next error is subtracting the left hand side of the equation and adding the right hand side

15x + 12y = 6

12x + 12y = 3

He wrote

3x = 9

Instead of 3x = 3