Identifying variable to eliminate

Question 1

How to determine the variable to eliminate

x + y = 1

2x - y = 1

Answer 1

It is best to eliminate the variable that has the same numerical value in the variable, which can be eliminated by simply adding or subracting

In this case eliminate y as you add it

y + (-y) = 0

Question 2

Which variable to eliminate

x + y = 1

2x + y = 3

Answer 2

In this case eliminate y as you subtract it

y - y = 0

Question 3

When variables you wish to eliminate are both positive, what operation do you do?

Answer 3

Subtraction, as

5 - 5 = 0

3 - 3 = 0

Question 4

When variables you wish to eliminate are both negative, what operation do you do?

Answer 4

Subtraction, as

(-5) - (-5) = 0

(-3) - (-3) = 0

Question 5

When variables you wish to eliminate have different sign, what operation do you do?

Answer 5

Addition, as

(5) + (-5) = 0

(-3) + (3) = 0

Question 6

When variables you wish to eliminate have different numerical value, what operation do you do?

x + y = 1 (1)

2x + 3y = 5 (2)

Answer 6

Multiply one or both equations, so that the variables are common

To make x the same, multiply equation (1) by 2

2x + 2y = 2

To make y the same, multiply equation (1) by 3

3x + 3y = 3

Question 7

To elimate x, what do you do?

x + y = 1 (1)

3x + 2y = 5 (2)

Answer 7

To make x the same, multiply equation (1) by 3

3x + 3y = 3

Question 8

To elimate y, what do you do?

x + y = 1 (1)

3x + 2y = 5 (2)

Answer 8

To make y the same, multiply equation (1) by 2

2x + 2y = 2

Question 9

To elimate y, what do you do?

2x + 5y = 7 (1)

3x + 2y = 5 (2)

Answer 9

To make y the same, multiply equation (1) by 2

4x + 10y = 14

To make y the same, multiply equation (2) by 5

15x + 10y = 25

Question 10

To elimate x, what do you do?

2x + 5y = 7 (1)

3x + 2y = 5 (2)

Answer 10

To make x the same, multiply equation (1) by 3

6x + 15y = 21

To make x the same, multiply equation (2) by 2

6x + 4y = 10