Question

5x + 7y + 2z = -79x + 7y + 2z = 52x - 7y - 5z = -2x = ?y = ?z = ?

Answer 1

Answer:

x = 3, y = -6, z = 10

Explanations:

The given equations are:

5x + 7y + 2z = -7..............(1)

9x + 7y + 2z = 5.................(2)

2x - 7y - 5z = -2......................(3)

Make x the subject of the formula in equation (1)

5x = -7 - 7y - 2z

x = ( -7 - 7y - 2z) / 5 ...........(4)

Substitute equation (4) into equations (2) and (3)

`\begin{gathered} 9((-7-7y-2z)/(5))+\text{ 7y + 2z = 5} \\ \text{Multiply through by 5} \\ 9(-7-7y-2z)\text{ + 35y + 10z = 25} \\ -63-63y-18z+\text{ 35y + 10z = 25} \\ 28y+8z\text{ = -}88 \\ 7y\text{ + 2z = -22}\ldots\ldots\ldots.(5) \end{gathered}`
`\begin{gathered} 2((-7-7y-2z)/(5))-7y-5z=-2 \\ \text{Multiply through by 5} \\ 2(-7-7y-2z)-35y-25z=-10 \\ -14-14y-4z-35y-25z\text{ = -}10 \\ 49y+29z\text{ = -4}\ldots\ldots\ldots(6) \end{gathered}`

Solve equations (5) and (6) simulataneously:

Make z the subject of the formula from equation (5), the equation becomes:

`\text{z = }(-22-7y)/(2)\ldots\ldots\ldots(7)`

Substitute equation (7) into equation (6)

`\begin{gathered} 49y\text{ + 29(}(-22-7y)/(2))=-4 \\ \text{Multiply through by 2} \\ 98y\text{ -}638-203y\text{ = -}8 \\ 105y\text{ = }8-638 \\ 105y\text{ = }-630 \\ y\text{ = }(-630)/(105) \\ y\text{ = -6} \end{gathered}`

Put the value of y into equation (7)

`\begin{gathered} z\text{ = }(-22-7(-6))/(2) \\ z\text{ = }(-22+42)/(2) \\ \text{z = }(20)/(2) \\ z\text{ = 10} \end{gathered}`

Put the value of z into equation (4)

`\begin{gathered} \text{x = }(-7-7y-2z)/(5) \\ x\text{ = }(-7-7(-6)-2(10))/(5) \\ x\text{ = }(-7+42-20)/(5) \\ x\text{ = }(15)/(5) \\ x\text{ = 3} \end{gathered}`