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3 years ago

Solve the system of linear equations by substitution

2 answers:

7 0

There is the equal values method, so you can do:

x-4 = 4x-10 (remove x from both sides)
-4 = 3x -10 (add ten to both sides)
6 = 3x (devide by 3x)
2 = x

Check: (by plugging it into the equation)
y = 2-4 and y = 8-10
y = -2 and y = -2
that's matches so it is correct...
YOUR ANSWER IS:
(2, -2)

I hoped I helped sort things out, and have a great day!

Anit [1.1K]3 years ago

5 0

Y = x-4
y = 4x-10

Compare both the equations,
4x-10 = x-4
4x-x = 10-4
3x = 6
x = 6/3
x = 2

Now, substitute it in 1st equation,
y = 2-4 = -2

In short, Your Answer would be (2, -2)

Hope this helps!

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Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction. Samuel traveled 3km/h fa

12345 [234]

Samuel was going with 40 km/h and Heather was going with 37 km/h

Step-by-step explanation:

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction

Samuel traveled 3 km/h faster than Heather
After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
Heather was 8 km ahead of Samuel

We need to find how fast each was going

Assume that Heather's speed is x km/h

∵ Heather's speed = x km/h

∵ Samuel traveled 3 km/h faster than Heather

∴ Samuel's speed = x + 3 km/h

The formula of the distance is distance = speed × time

∵ Samuel travel for 3.5 hours

- Find the distance that Samuel traveled in 3.5 h

∴ Samuel distance = (x + 3) × 3.5

- Multiply the bracket by 3.5 to simplify

∴ Samuel distance = 3.5x + 10.5

∵ Samuel took a break for half hour

∵ Heather kept going

∵ At the end of the break, Heather was 8 km ahead of Samuel

- That means Heather was going for 4 hours (3.5 + 0.5), and her

distance is longer than Samuel distance by 8 km

∴ Heather distance = x × 4 = 4x

- Subtract the distance of Samuel from the distance of Heather

and equate the difference by 8

∵ 4x - (3x + 10.5) = 8

∴ 4x - 3x - 10.5 = 8

- Add the like terms in the left hand side

∴ 0.5x - 10.5 = 8

- Add 10.5 to both sides

∴ 0.5x = 18.5

- Divide both sides by 0.5

∴ x = 37

∵ x represents Heather's speed

∴ Heather's speed = 37 km/h

∵ x + 3 represents Samuel's speed

∴ Samuel's speed = 37 + 3 = 40 km/h

Samuel was going with 40 km/h and Heather was going with 37 km/h

Learn more:

You can learn more about the equation of motion in brainly.com/question/568302

#LearnwithBrainly

3 0

3 years ago

I have to get this so I pass help plz

pshichka [43]

Answer:

$\boxed{\sf x=-2}$

$\boxed{\sf y=-4}$

Step-by-step explanation:

First, Let's solve for x in -2x+2y=-4:

$\sf -2x+2y=-4$

Subtract 2y from both sides:

$\sf -2x+2y-2y=-4-2y$

$\sf -2x=-4-2y$

Divide both sides by -2:

$\sf \cfrac{-2x}{-2}=-\cfrac{4}{-2}-\cfrac{2y}{-2}$

$\bold{ x=y+2}$

Now, we'll substitute x=y+2 to 3x+3y=-18:

$\sf 3x+3y=-18$

→ let x=2+y

$\sf 3\bold{(2+y)}+3y=-18$

Simplify:

$\sf 6+6y=-18$

Now, let's solve for y in 6+6y=-18

$\sf 6+6y=-18$

Subtract 6 from both sides:

$\sf 6+6y-6=-18-6$

$\sf 6y=-24$

Divide both sides by 6:

$\sf \cfrac{6y}{6}=\cfrac{-24}{6}$

$\bold{ y=-4}$

Now, substitute y=-4 into x=2+y:

$\sf x=2+y$

→ let y = -4

$\sf x=2+\bold{-4}$

$\bold{x=-2}$

Therefore, x=-2 and y=-4.

_____________________________________

5 0

2 years ago

alissa's monthly budget is $1500. she spends 30% on rent. How much does she spent on the rent? A)$250 B)300 C)450 D)500

I am Lyosha [343]

1500 × 0.30 = $450 (C)

3 0

3 years ago

Read 2 more answers

A juice recipe calls for 5 cups of grape juice for every 2 cups of peach juice are needed for a batch that uses 8 cups of peach

Ksivusya [100]

Answer: 20 cups of grape juice are needed for 8 cups of peach juice.

Step-by-step explanation:

5 times 4 is 20.

We must do this step because you need 2 cups for 1 batch, and times 4 that is 8. So then we multiplied 5 times 4.

So, 20 cups of grape juice are needed for 8 cups of peach juice.

Hope this answer helps you out!

3 0

3 years ago

Read 2 more answers

PLEASE PLEASE PLEASSE HELP I WILL MARK BRAINLIEST!!! FIRST TO GIVE A PROPER ANSWER WILL GET BRAINLIEST

juin [17]

Answer:

Answer to 9 is B answer to 10 is C

Step-by-step explanation:

Please give brainliest

7 0

3 years ago