Question

5. 3x + 5y + 5z =1 x - 2y = 5 2x + 4y = 11

Answer 1

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 = $\frac{21}{4\\}$

Substitute this value of x into (3)

2 × $\frac{21}{4\\}$ + 4y = 11

$\frac{21}{2\\}$ + 4y = 11 ( subtract $\frac{21}{2\\}$ from both sides )

4y = $\frac{1}{2}$ ( divide both sides by 4 )

y = $\frac{1}{8\\}$

Substitute the values of x and y into (1) and solve for z

3 × $\frac{21}{4\\}$ + 5 × $\frac{1}{8\\}$ + 5z = 1

$\frac{63}{4}$ + $\frac{5}{8}$ + 5z = 1

$\frac{131}{8}$ + 5z = 1 ( subtract $\frac{131}{8}$ from both sides )

5z = - $\frac{123}{8}$ ( divide both sides by 5 )

z = - $\frac{123}{40}$

Solution is

x = $\frac{21}{4\\}$, y = $\frac{1}{8\\}$, z = - $\frac{123}{40}$