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ozzi
3 years ago
8

Without drawing the graph, find out whether the lines representing the following pair of linear equations intersect at a point,

are parallel or coincident: 9x-10y=21
& 3/2x-5/3y=7/2
Mathematics
1 answer:
Rainbow [258]3 years ago
6 0

The easiest way to solve this question is to write out both equations in the form y = mx + c, where m is the gradient and c is the y-intercept.

a) Thus, if we start with 9x - 10y = 21, then we get:

9x - 10y = 21

(9/10)x - y = 21/10 (Divide both sides by 10)

(9/10)x = y + 21/10 (Add y to both sides)

(9/10)x - 21/10 = y (Subtract 21/10 from both sides)

Thus, our first equation may be written as y = (9/10)x - 21/10

b) Now if we take the second equation, (3/2)x - (5/3)y = 7/2, we can follow the same process to get:

(3/2)x - (5/3)y = 7/2

(9/10)x - y = 21/10 (Multiply each side by 3/5)

(9/10)x = y + 21/10 (Add y to each side)

(9/10)x - 21/10 = y (Subtract 21/10 both sides)

Thus, the second equation may be written as y = (9/10)x - 21/10.

Now you might have already realised this but the two equations are actually exactly the same; if they are the same line then they are said to be coincident.

Note that if the two lines are parallel, then their gradients (m) would be the same, but the y-intercepts (c) would be different (eg. y = 2x + 3 and y = 2x + 4 are parallel).

If they just intersect at a point, then the gradients of the lines would be different, but the y-intercepts could be the same or different (eg. y = 4x + 2 and y = 9x + 2 intersect at one point).

For them to be coincident however, both the gradient and y-intercept must be the same as only then would they be the same line.

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Y(a -b) =c(y+ a); y
Ksivusya [100]

Answer:

y = ac / (a - b - c)

Step-by-step explanation:

y(a - b) = c(y + a)

Distribute

ay - by = cy + ac

Subtract cy from both sides

ay - by - cy = ac

Factor out y

y(a - b - c) = ac

Divide both sides by (a - b - c)

y = ac / (a - b - c)

5 0
2 years ago
Use the multiplier method to increase 88 pounds by 14% you must show your working
Komok [63]

Answer:

100.32

Step-by-step explanation:

First, we have to find 14% of 88

14% of 88 is = 88 x 14/100

                  = 12.32

Now we have to increase the number 88 by 14%, which means we have to add 14% of 88 (12.32) to the given number (88)  

88 + (14% of 88)

= 88 + 12.32

=100.32 pounds

6 0
1 year ago
If rounded to the nearest tenth 47.098
Nataliya [291]
47.098 rounded to the nearest tenth is 47.1
3 0
2 years ago
WHAT IS 3847 TIMES 4387 AND PLAESE ROUND!!!!!<br> ---------<br> 82364
Andrew [12]

Answer:

16,876,789. 82364 ≈ 82,000

Step-by-step explanation:

Let's go through this Step by Step.

3847 * 4387 =\\3847 * 7 = 26929\\3847 * 80 = 307,760\\3847 * 300 = 1,154,100\\3847 * 4000 = 15,388,000

Now let's go through the Addition.

26929 + 307,760 = 334,689\\334,689 + 1,154,100 = 1,484,789\\1,484,789 + 15,388,000 = 16,872,789

Now, we round 82364 to the nearest thousand.

The nearest thousand is 2000. so the answer to this one would be 82000.

hope this helps.

6 0
2 years ago
Read 2 more answers
HELP I WILL MARK YOU AS A BRAINLIEST!
vfiekz [6]
$6.90 divided by 3 is $2.30 which is the unit rate and if you multiply $2.30 by 10 you get $23
3 0
3 years ago
Read 2 more answers
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