What is the answer to 8x - 6z = 38 ,
2x - 5y + 3z = 5 , x + 10y - 4z = 8?
1) 8x - 6z = 38
2) 2x - 5y + 3z = 5
3) x + 10y - 4z = 8
Multiply equation two by 2 and add to equation one.
2 * (2x - 5y + 3z) = 5 * 2
4x - 10y + 6z = 10
+(8x - 6z = 38)
-----------------------------
12x - 10y = 48
4) 12x - 10y = 48
Multiply equation two by 4.
4 * (2x - 5y + 3z) = 5 * 4
5) 8x - 20y + 12z = 20
Multiply equation three by 3.
3 * (x + 10y - 4z) = 8 * 3
6) 3x + 30y - 12z = 24
Add equation six to equation five.
8x - 20y + 12z = 20
+(3x + 30y - 12z = 24)
---------------------------------
11x + 10y = 44
7) 11x + 10y = 44
By adding equation seven to equation four, we
can eliminate y, and solve for x.
12x - 10y = 48
+(11x + 10y = 44)
--------------------------
23x = 92
23x = 92
x = 4 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
We can plug that into both equation four and
equation seven, solving for y and verifying at
the same time.
Four:
12x - 10y = 48
12(4) - 10y = 48
48 - 10y = 48
-10y = 48 - 48
-10y = 0
y = 0 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Seven:
11x + 10y = 44
11(4) + 10y = 44
44 + 10y = 44
10y = 44 - 44
10y = 0
y = 0 same answer for y
We can substitute both of those values into the
original three equations to solve for z. Using
all three equations gives us the chance to verify
the results.
One:
8x - 6z = 38
8(4) - 6z = 38
32 - 6z = 38
-6z = 38 - 32
-6z = 6
z = -1 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Two:
2x - 5y + 3z = 5
2(4) - 5(0) + 3z = 5
8 - 0 + 3z = 5
3z = 5 - 8
3z = -3
z = -1 same answer for z
Three:
x + 10y - 4z = 8
(4) + 10(0) - 4z = 8
4 + 0 - 4z = 8
-4z = 8 - 4
-4z = 4
z = -1 and verified again
x = 4, y = 0, z = -1
Why did they have y equal to zero? To cloud your
thinking, to confuse the issue, to see if you would
stay with it or walk away. There are times when
y is zero; it is unavoidable. Accept it.