Solve but don't graph?

Question

4x - 3y + z = 16
x + 2y - z = -3
3x + y +2z = 1

Answer 1

I would start by adding equations 2 and 3:

x + 3x + 2y + y -z + 2z = -3 + 1
4x + 3y + z = -2

Now subtract this from the first equation and you will cancel two variables:

4x - 4x - 3y - 3y + z - z = 16 - (-2)
-6y = 18
y = 18 / -6
y = -3

Now add equations 1 and 2 to eliminate z:

4x + x - 3y + 2y + z - z = 16 + (-3)
5x - y = 13

Plug in the y value from above:
5x - (-3) = 13
5x + 3 = 13
5x = 10
x = 10 / 5
x = 2

Then just plug x and y into any equation to get z:

x + 2y - z = -3
(2) + 2(-3) - z = -3
2 - 6 - z = -3
-4 - z = -3 (multiply by -1)
4 + z = 3
z = 3 - 4
z = -1

So your final answer is:
x = 2
y = -3
z = -1

Double-check by putting these values into each equation.
4x - 3y + z = 16
4(2) - 3(-3) + (-1) =? 16
8 + 9 - 1 =? 16
16 = 16 check

x + 2y - z = -3
(2) + 2(-3) - (-1) =? -3
2 - 6 + 1 =? -3
-3 = -3 check

3x + y + 2z = 1
3(2) + (-3) + 2(-1) =? 1
6 - 3 - 2 =? 1
1 = 1 check

So indeed, the answer is correct:
x = 2
y = -3
z = -1

Answer 2

4x - 3y + z = 16 (1)
x + 2y - z = -3 (2)
3x + y +2z = 1 (3)

(1)+(2)
5x - y = 13 (4)

2(2)+(3)
5x + 5y = -5 (5)

(4)-(5)
-6y = 18
y = -3

sub y=-3 into (5)
5x -15 = -5
5x = 10
x = 2

sub y=-3 and x=2 into (1)
8 + 9 + z = 16
z = -1

x=2
y=-3
z=-1

Answer 3

a million) -10x=5y could be switched over into the slope-intercept kind (y=mx+b) the place m is the slope of the right this moment line (m=upward thrust/run=y/x) and b as a results of fact the y-intercept, it somewhat is component to intersection of the line and the y-axis. -10x=5y is comparable to y=-10x/5=-2x+0. right here b is 0 and the slope is -2, meaning the line passes via the beginning place and leans on the left at a fee of two upward thrust to a minimum of one run. 2) 2x-3y=6 could be solved by using an identical answer as above or you need to use the intercept-kind. basically divide the consistent 6 by using the coefficients of x and y, 2 and -3,respectively, to locate the x and y-intercepts. So the x and y-intercept are 3 and -2. respectively. To graph the line, plot the intercepts (3,0) and (0,-2) on the Cartesian airplane then connect those factors, the line could be prolonged infinitely.

Answer 4

4x - 3y + z = 16 -----------eqn(1)

x + 2y -z = -3 -------------eqn(2)

3x + y + 2z = 1 -------------eqn(3)

add (1) and (2)

5x - y = 13 ---------eqn (4)

multiply eqn(2) with 2

2x + 4y - 2z = -6 --------eqn(5)

add (5) and (3)

5x + 5y = -5 ---------eqn(6)

x + y = -1 -------------eqn(7)
subtract (6) from (4)

- 6y = 18

y = -3

substitute in eqn(7)

x -3 = -1

x = 2

substitute x and y values in eqn(2)

2 - 6 - z = -3

-z = 1

z = -1

the values are x = 2, y = -3 and z = -1

Answer 5

4x - 3y + z 16
x + 2y - z = -3
-----------------
5x - y = 13

8x - 6y + 2z = 32
3x + y + 2z = 1
--------------------
5x - 7y = 31

5x - y = 13
5x - 7y = 31
-----------------
6y = -18
y = -3

5x - (-3) = 13
5x + 3 = 13
5x = 10
x = 2

4(2) - 3(-3) + z = 16
8 + 9 + z = 16
17 + z = 16
z = -1