Question

solve the following system of equations using substitution x+y+z=7y=32x+y-z=5enter your answer in the form of (x,y,z)

Answer 1

Given equations:

`x+y+z=7\ldots(1)`
`y=3\ldots(2)`
`2x+y-z=5\ldots(3)`

Substitute 3 for y in equation (1);

`\begin{gathered} x+3+z=7 \\ x+z=7-3 \\ x+z=4\ldots(4) \end{gathered}`

Substitute 3 for y in equation (3);

`\begin{gathered} 2x+3-z=5 \\ 2x-z=5-3 \\ 2x-z=2\ldots(5) \end{gathered}`

Adding equation (4) and (5);

`\begin{gathered} (x+z)+(2x-z)=4+2 \\ x+z+2x-z=6 \\ 3x=6 \\ x=(6)/(3) \\ x=2 \end{gathered}`

Substitute 2 for x in equation (4);

`\begin{gathered} 2+z=4 \\ z=4-2 \\ z=2 \end{gathered}`

Therefore, the values of (x,y,z) is (2,3,2).