Answer:
see explanation
Step-by-step explanation:
Given the 3 equations
3x + 5y + 5z = 1 → (1)
x - 2y = 5 → (2)
2x + 4y = 11 → (3)
Use (2) and (3) to solve for x and y
Multiply (2) by 2
2x - 4y = 10 → (4)
Add (3) and (4) term by term
4x = 21 ( divide both sides by 4 )
x = [tex]\frac{21}{4\\}[/tex]
Substitute this value of x into (3)
2 × [tex]\frac{21}{4\\}[/tex] + 4y = 11
[tex]\frac{21}{2\\}[/tex] + 4y = 11 ( subtract [tex]\frac{21}{2\\}[/tex] from both sides )
4y = [tex]\frac{1}{2}[/tex] ( divide both sides by 4 )
y = [tex]\frac{1}{8\\}[/tex]
Substitute the values of x and y into (1) and solve for z
3 × [tex]\frac{21}{4\\}[/tex] + 5 × [tex]\frac{1}{8\\}[/tex] + 5z = 1
[tex]\frac{63}{4}[/tex] + [tex]\frac{5}{8}[/tex] + 5z = 1
[tex]\frac{131}{8}[/tex] + 5z = 1 ( subtract [tex]\frac{131}{8}[/tex] from both sides )
5z = - [tex]\frac{123}{8}[/tex] ( divide both sides by 5 )
z = - [tex]\frac{123}{40}[/tex]
Solution is
x = [tex]\frac{21}{4\\}[/tex], y = [tex]\frac{1}{8\\}[/tex], z = - [tex]\frac{123}{40}[/tex]
