Substitution method

Question 1

Choose the subject to make as an unknown from any of the 2 equations

x + y = 2 (1)

2x + y = 3 (2)

Answer 1

If y is the subject, from equation 1

y = 2 - x

If x is the subject, from equation 1

x = 2 - y

Question 2

Choose the subject to make as an unknown from any of the 2 variables from equation (1)

4x + y = 5 (1)

2x - y = 3 (2)

Answer 2

If y is the subject, from equation 1

y = 5 - 4x

If x is the subject, from equation 1

4x = 5 - y

x = (5 - y)/4

Question 3

Choose the subject to make as an unknown from any of the 2 variables from equation (2)

4x + y = 5 (1)

2x - y = 3 (2)

Answer 3

If y is the subject, from equation 2

y = 2x + 3

If x is the subject, from equation 2

2x = 3 + y

x = (3 + y)/2

Question 4

After making a variable as a subject, substitute that in the other equation

y = 5 - 4x (1)

2x - y = 3 (2)

Answer 4

Substitute y = 5 - 4x into equation 2

2x - (5 - 4x) = 3

Question 5

After making a variable as a subject, substitute that in the other equation

x = (5 - y)/4 (1)

2x - y = 3 (2)

Answer 5

Substitute x = (5 - y)/4 into equation 2

2* (5 - y)/4 - y = 3

Question 6

After making a variable as a subject, substitute that in the other equation

y = 2x - 3 (1)

4x + y = 5 (2)

Answer 6

Substitute y = 2x - 3 into equation 2

4x + (2x - 3) = 5

Question 7

Find the value of the unknown in the new equation

2x - (5 - 4x) = 3

Answer 7

2x - (5 - 4x) = 3

2x - 5 + 4x = 3

2x + 4x = 3 + 5

6x = 8

x = 3/4

Question 8

Finally substitute the known value into the equation to find the other unknown

when x = 3/4

y = 5 - 4x

Answer 8

y = 5 - 4 * 3/4

= 5 - 3

= 2