Solving systems of linear equations in 3 variables...
1) 3x-2y+2z=1
2) 2x+5y-5z=7
3) 4x-3y+z=-3
I combined 1 and 3 to get -5x+4y=7
And then i combined 2 and 3 to get
-13y+11z=-17. Can that be right? how would you combine those two equations?
you should when combining 2 and 3, multiply to get rid of z, so multiply 3 by 5, then add.
You would like to have the same two variables in the two new equations.
Your first one contains x and y, but your second contains y and z. This gets you nowhere.
Your first equation is ok,
Now take 5 times the third and add it to the second.
So you would get 22x-10y=-8? how would you combine that with -5x+4y=7?
THanks guys! i get it now!
To combine the equations 1) and 3) correctly, you need to make sure that the coefficients of the x or z terms are the same. Let's go through the steps:
1) 3x - 2y + 2z = 1
3) 4x - 3y + z = -3
To eliminate the x term, you can multiply equation 1) by 4 and equation 3) by 3:
4 * (3x - 2y + 2z) = 4 * 1
3 * (4x - 3y + z) = 3 * (-3)
Which simplifies to:
12x - 8y + 8z = 4
12x - 9y + 3z = -9
Now, you can subtract the second equation from the first equation:
(12x - 8y + 8z) - (12x - 9y + 3z) = 4 - (-9)
This simplifies to:
12x - 8y + 8z - 12x + 9y - 3z = 4 + 9
Combining like terms, it becomes:
(-8y + 9y) + (8z - 3z) = 13
y + 5z = 13
So, you combined equations 1) and 3) incorrectly. The correct combination is y + 5z = 13.
To combine equations 2) and 3), you follow a similar process. Let's go through the steps:
2) 2x + 5y - 5z = 7
3) 4x - 3y + z = -3
To eliminate the x term, you can multiply equation 2) by 2 and equation 3) by -4:
2 * (2x + 5y - 5z) = 2 * 7
-4 * (4x - 3y + z) = -4 * (-3)
Which simplifies to:
4x + 10y - 10z = 14
-16x + 12y - 4z = 12
Now, you can add the second equation to the first equation:
(4x + 10y - 10z) + (-16x + 12y - 4z) = 14 + 12
This simplifies to:
4x - 16x + 10y + 12y - 10z - 4z = 26
Combining like terms, it becomes:
(4x - 16x) + (10y + 12y) + (-10z - 4z) = 26
-12x + 22y - 14z = 26
So, you combined equations 2) and 3) correctly, and the result is -12x + 22y - 14z = 26.
To summarize the combined equations:
1) -5x + 4y = 7
2) -12x + 22y - 14z = 26
Let me know if there's anything else I can help you with!