How do you solve 2x-y=3 and x+2y=24 using substitution?

2 Answers
Mar 30, 2018

2x - y = 3
x + 2y = 24

Substitution is a method for solving algebraic equations by finding the value of a variable in terms of other variables and substituting that value into existing equations.
x = 24 - 2y

Substituting 24 - 2y for x in the first equation:

2(24-2y) - y = 3
48 -4y - y = 3
5y = 48-3
5y =45
y = 9

Substituting 9 for y in the second equation:
x + 2*9 = 24
x = 24 - 18
x = 6

Mar 30, 2018

x=6 and y=9.

Explanation:

2x-y=3" " " "(1)
x+2y=24" " " "(2)

From eqn (2)

x=24-2y" " " "(3)

Sub eqn (3) into eqn (1)

2(24-2y)-y=3

48-4y-y=3

45=5y

y=9

Sub y=9 into eqn (2)

x=24-2(9)

x=6