X+ y = 10
2x = 2y+4
2x/2 = 2/2y+4/2
x = y + 2
x+y = 10
y+2+y=10
2y + 2 = 10
2y +2-2 =10-2
2y = 8
2y/2 =8/2
y = 4
x + y =10
x + 4 =10
x +4-4 =10-4
x = 6
Check
2x = 2y +4
2(6) = 2(4) +4
12 = 8+4
12= 12
Answer:
a) 0.8( 8/10 gives 0.8)
b)0.7( if it was 7/100 it would have been
0.07)
c)3.5( by converting mixed fractions to improper fractions, that is, 3×2+1 and having the same denominator 2… we get 7/2… for the purpose of converting it to decimal, 7×5/2*5= 35/10… by moving one decimal place to the left, we get 3.5)
D) 2.5 ( the same way as c) 5*5/2*5: 25/10 or you can make it to be 5*50/2*50: 250/100 which still gives 2.5)
Answer:
x = -2 and y = 3
{y = -3 x - 3, y = (3 x)/4 + 9/2} = x = -2 and y = 3
Step-by-step explanation:
Solve the following system:
{6 x + 2 y = -6
3 x - 4 y = -18
Express the system in matrix form:
(6 | 2
3 | -4)(x
y) = (-6
-18)
Solve the system with Cramer's rule:
x = -6 | 2
-18 | -4/6 | 2
3 | -4 and y = 6 | -6
3 | -18/6 | 2
3 | -4
Evaluate the determinant 6 | 2
3 | -4 = -30:
x = -6 | 2
-18 | -4/(-30) and y = 6 | -6
3 | -18/(-30)
Simplify -6 | 2
-18 | -4/(-30):
x = -1/30 -6 | 2
-18 | -4 and y = 6 | -6
3 | -18/(-30)
Simplify 6 | -6
3 | -18/(-30):
x = -(-6 | 2
-18 | -4)/30 and y = -1/30 6 | -6
3 | -18
Evaluate the determinant -6 | 2
-18 | -4 = 60:
x = (-1)/30×60 and y = -(6 | -6
3 | -18)/30
(-1)/30×60 = -2:
x = -2 and y = -(6 | -6
3 | -18)/30
Evaluate the determinant 6 | -6
3 | -18 = -90:
x = -2 and y = (-1)/30×-90
(-1)/30 (-90) = 3:
Answer: x = -2 and y = 3
___________________________________________
Solve the following system:
{y = -3 x - 3
y = (3 x)/4 + 9/2
Express the system in standard form:
{3 x + y = -3
-(3 x)/4 + y = 9/2
Express the system in matrix form:
(3 | 1
-3/4 | 1)(x
y) = (-3
9/2)
Write the system in augmented matrix form and use Gaussian elimination:
(3 | 1 | -3
-3/4 | 1 | 9/2)
Add 1/4 × (row 1) to row 2:
(3 | 1 | -3
0 | 5/4 | 15/4)
Multiply row 2 by 4/5:
(3 | 1 | -3
0 | 1 | 3)
Subtract row 2 from row 1:
(3 | 0 | -6
0 | 1 | 3)
Divide row 1 by 3:
(1 | 0 | -2
0 | 1 | 3)
Collect results:
Answer: {x = -2
, y = 3
Answer:
The answer is D
(x=3, y=8)
Step-by-step explanation:
We want to reduce as many variable as we can so, we can obtain the value for the remaining variables.
Therefore, the first equation y=x+5 multiply it -2., you have -2y=-2x-10 and sum it to the second (2y-x=13), you will obtain the following: -x=13-2x-10.
You have x=3.
If you substitute x=3 in the first equation, you have y=8
Answer:
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