Word problem: solving with 3 variables:
Lila has three investments totaling $100,000. These investments earn interest at 7%, 9%, and 11% respectively. Lila's total income from these investments is $9800. The income from the 11% investment exceeds the total income from the other two investments by $1200. Find how much Lila has invested at 11%.
Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 40 cents each, oatmeal muffins at 45 cents each, and cranberry muffins at 50 cents each. Charles buys some of each kind and chooses twice as many cranberry muffins as chocolate chip muffins. If he spends $6.45 on 14 muffins, how many chocolate chip muffins did he buy?
Solve the following system. What is the value of y?
-5x - z = 2
x + 4y - 2z = 1
2x - 4y - z = -13
Solve the following system. What is the value of y?
-5x + 2z = 18
x + 4y + z = -25
-3x + 5y - z = -12
Solve the following system. What is the value of y?
-5x - z = 2
x + 4y - 2z = 1
2x - 4y - z = -13
Please help! I am so lost..
Honestly, I get stuck from the begining...
I have tried looking up examples online and this is what I get:
-5x + 2z = 18
x + 4y + z = -25
-3x + 5y - z = -12
-5x + 2z = 18
x + 4y + z = -25
-4x + 4y +32 = -7
x + 4y + z = -25
-3x + 5y - z = -12
-2x + 9y = -37
-4x + 4y + 3z = -7
-2x + 9y = -37
and then I am lost..
Isn't the good ol' Google working anymore?
Have a look here: System of linear equations - Wikipedia, the free encyclopedia
Okay, I tried them over again.. can you at least let me know if I got these examples right?
Solve the following system. What is the value of y?
4x - 5z = -33
x + y + 2z = 11
-x + 3y - z = 6
y = 5
Solve the following system. What is the value of y?
-5x + 2z = 18
x + 4y + z = -25
-3x + 5y - z = -12
y= -1
Solve the following system. What is the value of y?
-5x - z = 2
x + 4y - 2z = 1
2x - 4y - z = -13
y= 3
We start with this:
Switch the position of Eq1 & Eq2:
Multiply Eq1 by 5 and add the result to Eq2. Put the result in the Eq2 slot:
Divide Eq2 by 20:
Multiply Eq1 by -2 and add the result to Eq3. Put the result in the Eq3 slot:
Multiply Eq2 by 12 and add the result to Eq3. Put the result in the Eq3 slot:
Divide Eq3 by -3.6:
You can see how easy it is from here to find x and y. I'll let you do that. (If you can see the white dots in the equations above, ignore them. I only put them there to line things up.)
01
When I think of systems of equations with three variables, I usually just use the Gaussian Method of Elimination...which is right here: Systems of Linear Equations: Gaussian Elimination