Solve the system by substitution.
{-x - y - z = -8
{ -4x + 4y + 5z = 7
{ 2x + 2z = 4
Solve the system by elimination.
{-2x + 2y + 3z = 0
{-2x - y + z = -3
{2x+ 3y+ 3z = 5
So what the answer? I’m still confused. How would I do the full equations?
I got 6 from that first part not -6.. and I'm confused on what to do after you get the value of z not before ?? Can yall actually help or no cus so far u just confused my g right here and gave us the wrong answer AND didn't actually help with the rest of it
Why did the substitution method feel left out? Because it was feeling replaced!
Now, let's solve the system by substitution.
1) From the first equation, we can solve for x:
-x - y - z = -8
x = -8 + y + z
2) Substitute the value of x in the other two equations:
-4(-8 + y + z) + 4y + 5z = 7
2(-8 + y + z) + 2z = 4
Now, let's solve the system by elimination.
1) Let's add the first and second equations:
(-2x + 2y + 3z) + (-2x - y + z) = 0 + (-3)
-4x + 2y + 4z = -3
2) Let's subtract the second equation from the third equation:
(2x + 3y + 3z) - (-2x - y + z) = 5 - (-3)
4x + 4y + 2z = 8
Well, that wasn't very funny, was it? Let's hope the solution is!
Back to solving, we now have a system of two equations:
-4x + 2y + 4z = -3
4x + 4y + 2z = 8
If we add these two equations, the x terms will cancel out:
-4x + 2y + 4z + 4x + 4y + 2z = -3 + 8
6y + 6z = 5
Divide both sides by 6:
y + z = 5/6
Substitute this result back into one of the original equations. Let's choose the first one:
-x - (5/6) = -8
-x = -8 + (5/6)
-x = -43/6
Multiply both sides by -1 to solve for x:
x = 43/6
Therefore, the solution is:
x = 43/6, y + z = 5/6
And let's not forget about our elimination solution:
y + z = 5/6
Since we didn't eliminate any of the variables, the system remains unchanged.
Well, I hope that brought a smile to your face! Let me know if you have any other questions.
1st question- y=6 x=3 z=-1
2x=4-2z
x=-z+2-(z-2)-y-z=-8
-2-y=-8
y=6-4(-z+2)+4(6)+5z=7
4z-8+24+5z=7
9z+16=7
2x+2(-1)=4
2x-2=4
I mean he used substitution first. That gave z = -6. Then the link will help with elimination.
Using the first equation, -x=y+z-8
and substituting that into the others, you have
4(y+z-8)+4y+5z = 7
-2(y+z-8)+2z = 4
or,
8y+9z = 39
-2y = 12
and the rest is easy
For the elimination, start by subtracting row1 from row2, and adding row1 to row3. That gives you
-2x+2y+3z = 0
0 -3y-2z = -3
0 +5y+6z = 5
Now work with row 2 to get rid of the y in row3, and then you have z, and you can then find y and x.
Steve showed you how to do it with elimination. You got z = -6. Now go back and get x and y
for the second one try the Gauss/Jordan link I gave you for the procedure.
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx