Combination method: add the two equations together
5) <span>4x-9y=1 6) 3x - 2y = 14
+( - 4x+6y=-2 ) + (2x + 2y = 6)
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0 - 5y = -1 5x + 0 = 20
-5y = -1 5x = 20
isolate the y isolate the x
-5y / -5 = -1/-5 5x/5 = 20/5
y = 1/5 x = 4
</span>4x-9y=1 3x - 2y = 14
4x - 9(1/5) = 1 3(4) - 2y = 14
4x - 9/5 = 1 12 - 2y = 14
4x - 9/5 (+9/5) = 1 (+9/5) 12 (-12) - 2y = 14 (-12)
4x = 14/5 -2y = 2
4x/4 = 14/5(/4) -2y(/-2) = 2(/-2)
x = 14/20 y = -1
Elimination method
7) 4x + 3y = 29 + (5x + 2y = 24)
eliminate one of the variables by multiply the number to both sides
2 (4x + 3y = 29) + 3 (5x + 2y = 24)
8x + 6y = 58
-( 15x + 6y = 72)
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-7x = - 14
-7x/-7 = -14/-7
x = 2
4(x) + 3y = 29
4(2) + 3y = 29
3y + 8 = 29
3y + 8 (-8) = 29 (-8)
3y = 21
3y/3 = 21/3
y = 7
8) like #7, you must eliminate one of the variables by multiply the number to both sides
-4x - 2y = 14
-10x + 7y = -25
7(-4x - 2y = 14)
-2(-10x + 7y = -25)
-28x - 14y = 98
- (20x -14y = -25)
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-48x = 123
-48x/-48 = 123/-48
x = -2.56
-4(-2.56) - 2y = 14
10.24 - 2y = 14
10.24(-10.24) - 2y = 14 (-10.24)
-2y = 3.76
-2y/-2 = 3.76/-2
y = -1.88
hope this helps
Answer:
6/0
Step-by-step explanation:
1. 0
2. 0
3.0
4. it can't divide
Answer:
15th term = 116
Step-by-step explanation:
a= 4
Sum of an A.P = n/2 {2a + (n-1)d}
sum of first five term is equal to one-fourth of the sum of the next five term
5/2{ 2*4 + (5-1)d} = 1/4 × 10/2{2*4 + (10-1)d
5/2 {8 + 4d} = 1/4 × 5{ 8 + 9d}
40/2 + 20/2d = 1/4{ 40 + 45d)
20 + 10d= 40/4 + 45/4d
20 + 10d = 10 + 45/4d
20 - 10 = 45/4d - 10d
10 =45d - 40d /4
10 = 5/4d
Divide both sides by 5/4
10 ÷5/4 = d
10×4/5 = d
40/5 = d
8 = d
d= 8
Find the 15th term
15th term = a + (n-1)d
= 4 + (15-1)8
= 4 + (14)8
= 4 + 112
= 116
The 15th term is 116
The coordinates of the midpoint are the average of the coordinates of the given points.
So, the x coordinate of the midpoint is the average of the x coordinates of the given point:
And similarly, the y coordinate of the midpoint is the average of the y coordinates of the given point:
So, the midpoint is the point
Answer:
(3, 3 )
Step-by-step explanation:
Given the 2 equations
3x - y = 6 → (1)
6x + y = 21 → (2)
Adding the 2 equations term by term will eliminate y, that is
(6x + 3x) + (y - y) = (21 + 6), that is
9x = 27 (divide both sides by 9 )
x = 3
Substitute x = 3 into either (1) or (2) and solve for y
Using (2), then
(6 × 3) + y = 21
18 + y = 21 ( subtract 18 from both sides )
y = 3
Solution is (3, 3 )