I need help please ASAP Please!!?

Question

Solve the system of equations. Write the solution as an ordered TRIPLE of the form (x,y,z)

2x+ 3y-z=17

Y=-3z-7

2x=x+ 2

I will give you best answer!

Answer 1

Let's start by plugging the second equation into the first:

y = -3z - 7

2x + 3y -z = 2x + 3*(-3z - 7) -z = 17 | Substitution

So now we've reduced it to two variables. Let's find x in terms of z:

2x - 9z - 21 - z = 17 | Given

2x -10z = 38 | Add 21 to both sides, combine z

x = (1/2)(38 + 10z) | Solve for x

Now, let's plug our expression for x into the last equation:

2x = x + 2

2(1/2)(38 + 10z)=(1/2)(38+10z) + 2 | Substitute (1/2)(38 + 10z) for x

38 + 10z = 19 + 5z + 2 | Simplify both sides

38 + 10z = 21 + 5z

5z = -17

z = -17/5

And carry on from there:

y = -3z - 7

y = -3(-17/5) -7 | Substitute -17/5 for z

y = 51/5 - 7 = 16/5

2x + 3y - z = 17 | Back to the first equation

2x + 3(16/5) - (-17/5) = 17 | Substitute 16/5 for y and -17/5 for z

2x + 65/5 = 17

2x = 4

x = 2

And so your final answer is: (2, 16/5, -17/5).

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