Q1. The answer is x = 1, y = 1, z = 0
<span>(i) -2x+2y+3z=0
</span><span>(ii) -2x-y+z=-3
</span>(iii) <span>2x+3y+3z=5
</span><span>_________
Sum up the first and the third equation:
</span>(i) -2x+2y+3z=0
(iii) 2x+3y+3z=5
_________
5y + 6z = 5
Sum up the second and the third equation:
(ii) -2x-y+z=-3
(iii) 2x+3y+3z=5
_________
2y + 4z = 2
(iv) 5y + 6z = 5
(v) 2y + 4z = 2
________
Divide the fifth equation by 2
(iv) 5y + 6z = 5
(v) y + 2z = 1
________
Multiple the second equation by -3 and sum the equation
(iv) 5y + 6z = 5
(v) -3y - 6z = -3
________
2y = 2
y = 2/2 = 1
y + 2z = 1
1 + 2z = 1
2z = 1 - 1
2z = 0
z = 0
-2x-y+z=-3
-2x - 1 + 0 = -3
-2x = -3 + 1
-2x = -2
x = -2/-2 = 1
Q2. The answer is x = -37, y = -84, z = -35
<span>(i) x-y-z=-8
(ii) -4x+4y+5z=7
(iii) 2x+2z=4
______
</span>Divide the third equation by 2 and rewrite z in the term of x:
(iii) x+z=2
z = 2 - x
______
Substitute z from the third equation and express y in the term of x:
<span>x-y-(2-x)=-8
x - y - 2 + x = 8
2x - y = 10
y = 2x - 10
______
Substitute z from the third equation and y from the first equation into the second equation:
</span><span>-4x + 4y + 5z = 7
-4x + 4(2x - 10) + 5(2 - x) = 7
-4x + 8x - 40 + 10 - 5x = 7
-x -30 = 7
-x = 30 + 7
x = -37
y = 2x - 10 = 2*(-37) - 10 = -74 - 10 = -84
z = 2 - x = 2 - 37 = -35</span>
Lol I had this kind of stuff, but now I’m in 7th)) Rationals are numbers that can be made into fractions, but almost all of the others can be made into it too, except for irrational. Sorry if I didn’t make sense
x = 8
Explanation:
AE = 3x - 4
EC = x + 12
SInce diagonals AC and DB intersect at E
it means the lines which meet at the intersection E are equal. A and C meet at E which gives AE and EC
AE = EC
3x - 4 = x + 12
collect like terms:
3x - x = 12 + 4
2x = 16
divide both sides by 2:
2x/2 = 16/2
x = 8
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
Using the scale factor, we have ...
x/8 = 0.25/1
x = 8(0.25) . . . . multiply by 8
x = 2
_____
<em>Additional comment</em>
I like to write proportions with the variable in the numerator. That way they are easily solved by a single multiplication. The trick is to get corresponding parts in the same positions. Here, the fractions are written ...
B/A = smaller part / larger part = x/8 = 0.25/1
An excluded value is one where the bottom of the fraction = 0.
In your case 1-3x=0
1=3x
x=1/3
At this point, the function does not exist. If you were to draw a graph of it, there wouldn't be a y-value corresponding to x=1/3.
