solving using elimination?

Question

x+y=5
y+z=10
x+z=9

Answer 1

x+y=5
y+z=10
x+z=9

solve for z

-1(x+y=5)(equation 1)
z+y=10(equation 2)

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-x-y=-5
z+y=10
----------------
-x+z=5(let us name this as equation 4)


x+z=9(equation 3)
-x+z=5(equation 4)
---------------------------
2z=14
2z/2=14/2

z=7


solve for x(use equation 3)

x+7(value of z we got)=9
x=9-7

x=2



solve for y(use equation 1)

2(value of x we got)+y=5
y=5-2

y=3

Answer 2

x + y = 5
y + z = 10
x + z = 9

The key to solving this using elimination is to eliminate a variable from the first two equations, and using the resulting equation with the third.

First, let's use elimination on the first two equations.

x + y = 5
y + z = 10

Subtract the first equation with the second, to obtain

(x + y) - ( y + z) = 5 - 10
x - z = -5

Now, couple this with the third equation.

x - z = -5
x + z = 9

Add these two equations together,to eliminate the z variable, to obtain

2x = 4. Therefore
x = 2

Use those same two equations

x - z = -5
x + z = 9

Subtract them, to eliminate the x variable.

-2z = -5 - 9
-2z = -14
z = 7

Now that we have x = 2 and z = 7, it is trivial to get y.

Since y + z = 10 and z = 7, then
y + 7 = 10, so y = 3

x = 2, y = 3, z = 7

Answer 3

Let's work with the first two equations:
x+y=5
y+z=10

x+y-(y+z)=5-10
x-z=-5

x-z=-5
x+z=9
=====
2x=4
x=2

2+z=9
z=7

y+7=10
y=3

The solution set is (2,3,7)

Check:
2+3=5
5=5

3+7=10
10=10

2+7=9
9=9

I hope this helps!

Answer 4

what Puggy said.