Answer:
[tex]x = 3.875[/tex]
[tex]y = 2.375[/tex]
Step-by-step explanation:
See comment for complete question.
Given
A.
[tex]x + 3y = 11 => x + 3y = 11[/tex]
[tex]5x - y = 17 => 15x - 3y = 51[/tex]
[tex]16x = 62[/tex]
B.
[tex]x + 3y = 11[/tex]
[tex]16x = 62[/tex]
Required
Determine the values of x and y
The first equation in B is:
[tex]x + 3y = 11[/tex]
In (a): 5x - y = 17 is multiplied by 3, then added to x + 3y = 11.
So, the second equation is:
[tex]5x - y = 17[/tex]
Solving (a) & (b):
[tex]x + 3y = 11[/tex] --- (1)
[tex]5x - y = 17[/tex] ---- (2)
Make x the subject in (1)
[tex]x + 3y = 11[/tex]
[tex]x = 11 - 3y[/tex]
Substitute [tex]11 - 3y[/tex] for x in [tex]5x - y = 17[/tex]
[tex]5(11 - 3y) - y = 17[/tex]
Open bracket
[tex]55 - 15y - y = 17[/tex]
[tex]55 - 16y = 17[/tex]
Collect Like Terms
[tex]- 16y = 17-55[/tex]
[tex]- 16y = -38[/tex]
Solve for y
[tex]y = \frac{-38}{-16}[/tex]
[tex]y = \frac{38}{16}[/tex]
[tex]y = 2.375[/tex]
Substitute 2.375 for y in [tex]x = 11 - 3y[/tex]
[tex]x = 11 - 3 * 2.375[/tex]
[tex]x = 11 - 7.125[/tex]
[tex]x = 3.875[/tex]
