Solve the system by elimination

Question

Solve the system of equations by elimination. Write as an ordered triple

x+y+z=10

2x-5y+7z=24

3x-7y=-15

Answer 1

Solving a system of 3 equations by elimination.

Answer 2

Our goal in elimiination method is to systematically get each variable to drop out by the use of +- coefficients so when combined they become zero. So we chose numbers to multiply the entire equations by based on wanting +# =(-#) =0.

first take the first two equations and eliminate the x variable .

1. multiply -2(x+y+z=10)--> -2x-2y-2z=-20 add this to the 2nd equation.
2. your result should be -7y +5z =4

Next take the second two equations and repeat the process on both to eliminate the x variable.

1. 3(2z-5y+7z=24). and -2(3x-7y=-15)
2. Your two resulting equations should then be 6x-15y+21z=72 and -6x +14y=30+5z=4
3. When you combine them-->. -y+21z=102

Now you should have two new equations with a y and z term each

1. -7y +5z =4. and
2. -y+21z=102

Next: multiply the 2nd equation by -7(-y +21z=102)--->7y-147z=-714

1. Now combine the first and altered 2nd equations.
2. -7y +5z =4 and 7y-147z=-714
3. The result will be -142z=-710---->Divide both sides by -142
4. z=5

Plug this answer into -7y +5z =4.--->. -7y+5(5) = 4---> -7y +25 =4 --> Subtractt 25 from both sides.

1. -7y = -21 --> Divide both sides by -7. -->. y =3

Finally, Take both your answers for y and z. and plug them into the original first equation and you will be able to solve for x.

1. x +3 +5 =10 -->Simplify --> x+8 = 10--> Subtract 8 from both sides and you get x=2

SO your ORDERED TRIPLE is (2,3,5)