At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
one approach using eqn1 find the expression for z then substitute in eqn 2 using this expression for z substitute in eqb 3 as well you will now have simultaneous eqn with 2 variables (x and y) there are about 4 methods to choose from to solve. Can you solve 2-variable eqn? with those values of x and y substitute in the expression for z to get that value, notice that if you add eqn 1 and eqn 3 you can elimiinate x work with this and let me know if you need more
eqn1: z = -2x-4y+1
im confused what to do next
gibe me a min let me find my glasses
\[2x+4y+z=1\]\[ -4x-2y+2z=22\]\[ -2x-6y-4z=-14\] I would start by adding equations 1 & 3. This will give you an equation only in terms of \(y\) and \(z\). Next, multiply equation 1 by \(2\) and add it to equation 2. This will give you another equation only in terms of \(y\) and \(z\). Call the first equation you got by combining equations equation A, and the second one equation B. Multiply equation A by 3 and add it to equation B. You should now have an equation in only 1 variable. Solve it for the value of that variable. Then use that value to work backwards through the equations to get the other two.
@whpalmer4 agree did not use the fastest I have x = -5
wait so it would be -2y-3z=-13 for eq 1 and 3?
Yes, so far so good!
how did you get Z
Which of us are you asking?
on my paper it says x = -5
no, \[-x =5\] means \[x = -5\]
she just forgot the - sign...
x = -5
i just don't get how to get Z
\[1: 2x+4y+z=1\]\[2: −4x−2y+2z=22\]\[3: −2x−6y−4z=−14\] Add equations 1 and 3 together: \[2x+(-2x)+4y+(-6y)+z+(-4z) = 1 + (-14)\]\[0x -2y -3z = -13\]\[A: -2y -3z = -13\] Next add 2*equation 1 + equation 2 together: \[2*2x + (-4x) + 2*4y + (-2y) + 2*z + 2z= 2*1 + 22\]\[0x + 6y + 4z = 24\]\[B: 6y + 4z = 24\] Now add 3*equation A + equation B together: \[3*(-2y) + 3(-3z) + 6y + 4z = 3*(-13) + 24\]\[0y - 5z = -15\]\[z = 3\] Plug \(z = 3\) into equation A or B and solve for \(y\): \[6y+4(3) = 24\]\[y=2\] Now plug \(z = 3,\ y=2\) into equation 1, 2 or 3 and solve for \(x\): \[2x+4(2)+(3)=1\]\[2x+11=1\]\[x=-5\] To verify this answer, you should put \((-5,2,3)\) into all 3 equations and verify that they work. That is a necessary condition for the solution to be correct.
Oooh I get it now, Thanks guys!
do you understand the general process?
Yep now I do, took me a while but i got it now
ok and as stated, always check the solution in the original. keep practicing!