2006-12-15 19:57:55 · 6 answers · asked by criminalinvestigator23 1 in Science & Mathematics ➔ Mathematics
2x + 5y = 31
4z - 3y = 21
z/x = 3
This is a system of equation, and your first step is to make everything linear. We have to multiply equation 3 by x on both sides to accomplish this.
2x + 5y = 31
4z - 3y = 21
z = 3x
Now, we move everything to the left hand side such that the equations are in the order of x, y, then z.
2x + 5y = 31
-3y + 4z = 21
-3x + z = 0
We can solve this many ways; I'm going to use substitution. From the third equation, z = 3x.
Substitute z = 3x into equation #2.
-3y + 4(3x) = 21, or 12x - 3y = 21, or
4x - y = 7.
Now we can solve for y from that equation: y = 4x - 7
And now, we can substitute y = 4x - 7 into equation #1.
2x + 5(4x - 7) = 31,
2x + 20x - 35 = 31
22x = 66
x = 3
Now that we have x = 3, we can plug this into equation 3 to get z.
-3x + z = 0, -3(3) + z = 0, -9 + z = 0, therefore z = 9
And now, we can plug in z = 9 into equation #2.
-3y + 4z = 21, -3y + 4(9) = 21, -3y + 36 = 21, -3y = -15, y = 5.
Therefore, x = 3, y = 5, z = 9
2006-12-15 20:24:55 · answer #1 · answered by Puggy 7 · 2⤊ 0⤋
X=3
Y=5
Z=9
2006-12-15 20:10:40 · answer #2 · answered by scorpion_tk04 3 · 2⤊ 0⤋
On the z/x=3 equation, multiply both sides by x:
z=3x
Now take the z=3x and substitute it into this problem:
4(3x)-3y=21
12x-3y=21
Subtract 12x on both sides:
-3y=-12x+21
Divide -3 on both sides:
y=4x-7
Now, substitute it into this equation:
2x+5(4x-7)=31
2x+20x-35=31
22x-35=31
22x=66
x=3
Find the y-value:
2(3)+5y=31
6+5y=31
5y=25
y=5
Find the z-value:
z/3=3
3(z/3)=3(3)
z=9
(3,5,9)
Check:
2(3)+5(5)=31
6+25=31
31=31
4(9)-3(5)=21
36-15=21
21=21
9/3=3
3=3
I hope that was helpful!
2006-12-16 06:07:10 · answer #3 · answered by Anonymous · 1⤊ 0⤋
x=3, y=5, z=9
2006-12-15 20:05:27 · answer #4 · answered by Reindeer Herder 4 · 2⤊ 0⤋
2x + 5y = 31
4z - 3y = 21
z/x=3
z = 3x
12x - 3y = 21
12x + 30y = 186
3y = 165
y = 5
2x + 25 = 31
2x = 6
x = 3
z = 9
36 - 15 = 21
2006-12-15 20:26:19 · answer #5 · answered by Helmut 7 · 2⤊ 0⤋
x=3
y=5
z=9
2006-12-15 20:06:05 · answer #6 · answered by star_unknown1 3 · 2⤊ 0⤋