Question

1. Given the system

2X + 3Y = 18

-2X + 5Y = 14

Explain how you would solve this system using combination. Give the solution as a coordinate pair (X,Y)

2. Given the system

3x + 4y = 5

2x +7y = 12

Explain how you would solve this system using combination. Give the solution as a coordinate pair (X,Y)

Answer 1

Answer:

1. (3,4)     2. (-1,2)

Step-by-step explanation:

1. We can solve this simultaneously:

2x + 3y = 18

-2x + 5y = 14 - we have to add the two equations

8y = 32

y = 4

Then we substitute y into one of the equations to get the value of x:

2x + 12 = 18

2x = 6

x = 3

So the answer is (3,4)

2. We can also solve this simultaneously:

3x + 4y = 5 - multiply this equation by 2

2x + 7y = 12 - multiply this equation by 3

6x + 8y = 10

6x + 21y = 36 - we subtract the equation above from this one

13y = 26

y = 2

Then we substitute y into one of the equations to get the value of x:

3x + 8 = 5

3x = -3

x = -1

So the answer is (-1,2)