Algebra question?

Question

Z-X=22

Y/X=7

Y+Z=70

what do X, Y, and Z equal?

Answer 1

First, put all three equations in standard form:

-x+z=22
-7x+y=0
y+z=70

Subtract 7 times the first equation from the second, and then multiply the first equation by -1:

x-z=-22
y-7z=-154
y+z=70

Subtract equation 2 from equation 3:

x-z=-22
y-7z=-154
8z=224

Divide equation 3 by 8:

x-z=-22
y-7z=-154
z=28

Add 7 times the third equation to the second and add the third equation to the first:

x=6
y=42
z=28

And we are done.

Answer 2

y/x=7 implies that y=7x. Rewriting Y+Z=70, we obtain 7x+z=70.

We thus have a system of linear equations:

z+7x=70
z-x=22

Subtracting the bottom equation from the top, we obtain 8x=48 or x = 6. from z-x=22, z-6=22 or z=28. Finally, y=7x or y=7*6 = 42

Answer 3

z-x=22 is the same as z=x+22
y/x=7 is the same as y=7x

you can plug these two "new" equations into your third equation to find what x equals

y+z=70 is x+22 + 7x = 70
8x+22=70
8x=48
x=6

then take z=x+22
z= 6+22
z=28

and y=7x
y=42

Answer 4

1. x = z - 22
2. y = 7x
3. z = 70 - y

Plug equation 2 in for y: z = 70 - 7x
now plug equation 1 in for x: z = 70 - 7(z-22)

solve for z: z = 70 - 7z + 154

z +7z = 224 - 7z + 7z

8z = 224

z = 56 plug this in to equation1. so you can get x

x = z - 22
x = 54 - 22
x = 32

Plug X and Z in to get Y in equation 2.

y = 7(32)
y = 224

Answer 5

Z-X = 22
X=Y/7
Z=70-Y
(70-Y)-(Y/7) = 22
7*[(70-Y)-(Y/7) = 22]
490 - 7Y -Y = 22*7
490-154 = 8Y
Y = 42

X= Y/7 = 42/7 = 6
Z=70-Y = 70-42 = 28

Answer 6

1st equation (finding x):
z - x = 22
x = z - 22

2nd equation (plug x, find y):
y/x = 7
y/(z -22) = 7
y = 7(z - 22)
y = 7z - 154

3rd equation (find z, plug y):
y + z = 70
7z - 154 + z = 70
8z = 224
z = 28

1st equation (plug z, find x):
28 - x = 22
x = 6

2nd equation (plug x, find y):
y/6 = 7
y = 42

Answer: x = 6, y = 42, z = 28

Answer 7

if we reorder z-x =22 , then z = 22+x
if we reorder y/x = 7 , then y = 7x
Put z = 22+x and y=7x into y +z = 70, it becomes 7x+(22+x)=70 ----> 8x+22=70 ----> 8x=70-22 ---> 8x=48 --> x=6
we put x=6 back to z = 22+x ---->z = 28
we put x=6 back to y=7x ----> y=42

Answer 8

3 equations can solve for 3 unknowns:
{z=22+x, y=7x, y=70-z}

7x=70-z
7x=70-(22+x)
7x=70-22-x
7x+x=48
8x=48
x=6

z=22+6
z=28

y=7(6)
y=42

Answer 9

They are variables that stand-in for numbers.
For example, where you have Z-X = 22, it states that whatever Z is, if you subtract 22 from it, you will get X.

Answer 10

Substitution is the most effective way of solving this question.

The answer is...
X=6
Y=42
Z=28

hope that helps...