Respuesta :
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)
[tex]\begin{gathered} 9(\frac{-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}[/tex][tex]\begin{gathered} 2(\frac{-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}[/tex]Solve equations (5) and (6) simulataneously:
Make z the subject of the formula from equation (5), the equation becomes:
[tex]\text{z = }\frac{-22-7y}{2}\ldots\ldots\ldots(7)[/tex]Substitute equation (7) into equation (6)
[tex]\begin{gathered} 49y\text{ + 29(}\frac{-22-7y}{2})=-4 \\ \text{Multiply through by 2} \\ 98y\text{ -}638-203y\text{ = -}8 \\ 105y\text{ = }8-638 \\ 105y\text{ = }-630 \\ y\text{ = }\frac{-630}{105} \\ y\text{ = -6} \end{gathered}[/tex]Put the value of y into equation (7)
[tex]\begin{gathered} z\text{ = }\frac{-22-7(-6)}{2} \\ z\text{ = }\frac{-22+42}{2} \\ \text{z = }\frac{20}{2} \\ z\text{ = 10} \end{gathered}[/tex]Put the value of z into equation (4)
[tex]\begin{gathered} \text{x = }\frac{-7-7y-2z}{5} \\ x\text{ = }\frac{-7-7(-6)-2(10)}{5} \\ x\text{ = }\frac{-7+42-20}{5} \\ x\text{ = }\frac{15}{5} \\ x\text{ = 3} \end{gathered}[/tex]