Answer:
[tex]x = 1[/tex] and [tex]y = 6[/tex]
Step-by-step explanation:
Given
[tex]2x + 3y = 20[/tex]
[tex]x + 5y = 31[/tex]
Required
Solve for x and y
Make x the subject in the second equation
[tex]x = 31 - 5y[/tex]
Substitute 31 - 5y for x in [tex]2x + 3y = 20[/tex]
[tex]2(31 - 5y) + 3y = 20[/tex]
[tex]62 - 10y + 3y = 20[/tex]
[tex]62 - 7y = 20[/tex]
Collect like terms
[tex]-7y = 20 - 62[/tex]
[tex]-7y = - 42[/tex]
Solve for y
[tex]y = \frac{-42}{-7}[/tex]
[tex]y = 6[/tex]
Substitute 6 for y in [tex]x = 31 - 5y[/tex]
[tex]x = 31 - 5 * 6[/tex]
[tex]x = 31 - 30[/tex]
[tex]x = 1[/tex]
