Answer: %0.00100010001
Step-by-step explanation:
The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
Answer: 
Step-by-step explanation:
Given
For figure (i) both triangles are congruent
For figure (ii)
Two triangles WXZ and WZY are congruent
Answer:
y = -½x + 5
Step-by-step explanation:
Formula for slope intercept form is y = mx + b
Where m represents the slope and b represents the y intercept
.............................
Solving for m
...........................
m = (y2 - y1)/(x2-x1)
y2 = 4, y1 = 2
x2 = 2, x1 = 6
m = (4-2)/2-6)
m = 2/(-4)
m = -½
.......................
Solving for b
.........................
Using point F(6,2) as reference
y = 2, x = 6, m = -½
if y = mx + b
Substituting 2 for y and 6 for x in the above equation
2 = -½ * 6 + b
2 = -3 + b
2 + 3 = b
5 = b
b = 5
OR
Using Point G(2,4) as reference
y = 4, x = 2, m = -½
if y = mx + b
Substituting 4 for y and 2 for x in the above equation
4 = -½*2 + b
4 = - 1 + b
4+1 = b
5 = b
b = 5
.............................................
Finally, we have to write the equation in slope form
Using y = mx + b
where m = -½ and b =5 ................ (Calculated)
y = -½x + 5
