Question

How do I check my answer algebraically? the system of equations was x+y+z=-1 2x=4y+z=1 x+2y-3z=-3 the answer I go twas z=1,y=2,x=-4

Answer 1

You have the correct solutions. You have a typing error on the second equation. It should be: `2x+4y+z=1`
`color(white)("dddd")"Not "2x=4y+z=1`

To format for spacing use: hash color(white)("ddd") hash
See https://socratic.org/help/symbols

Explanation:

`color(red)("The formatting of your question does not clearly differentiate")` `color(red)("between the different equations")`

Substitute your values back into the equations. If they work you are correct. If they don't work then you need to look for errorse in your working out or the writing down of the question.

`color(blue)("You got: "x=-4"; "y=2"; "z=1)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider LHS of `x+y+z=-1" "..................Equation(1)`

`(-4)+(2)+(1) -> -4+3=-1color(red)(larr" True")`
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Consider `2x=4y+z=1" ".................Equation(2)`

`2(-4)=4(2)+1=1 color(red)(larr" Clearly False!")`

Try a different structure `2x-4y+z=1`

`2(-4)-4(2)+1=1color(red)(larr" Clearly False!")`

Try a different structure `color(blue)(2x+4y+z=1)`

`2(-4)+4(2)+1=1 ->-8+8+1=1color(red)(larr" True")`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider `x+2y-3z=-3`

`(-4)+2(2)-3(1)=-3color(red)(larr" True")`