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Fed [463]
3 years ago
10

How to solve using substitution y=3/4X+5 4x-3y=-1

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
5 0
Please, use parentheses to enclose each fraction:
y=3/4X+5 should be written as <span>y=(3/4)X+5

Let's eliminate the fraction 3/4 by multiplying the above equation through by 4:

4[y] = 4[(3/4)x + 5]
Then 4y = 3x + 20
(no fraction here)

Let 's now solve the system   

4y=3x + 20
4x-3y=-1

We are to solve this system using subtraction.  To accomplish this, multiply the first equation by 3 and the second equation by 4.  Here's what happens:

12y = 9x + 60  (first equation)
16x-12y = -4, or -12y = -4 - 16x (second equation)

Then we have 

 12y = 9x + 60
-12y =-16x - 4

If we add here, 12y-12y becomes zero and we then have 0 = -7x + 56.
Solving this for x:  7x = 56; x=8

We were given equations   
</span><span>y=3/4X+5
4x-3y=-1

We can subst. x=8 into either of these eqn's to find y.  Let's try the first one:

y = (3/4)(8)+5 = 6+5=11

Then x=8 and y=11.

You should check this result.  Subst. x=8 and y=11 into the second given equation.  Is this equation now true?</span>
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3 years ago
Choose all the lines that are parallel to the line pictured in the graph bellow.
viktelen [127]

Answer:

a. y = -½x

b. y = -½x + 3

c. 2y = -x - 4

e. x + 2y = 8

Step-by-step explanation:

Parallel lines have the same slope. Therefore, the lines that will be parallel to the given line on the graph would have the same slope as the line of the graph.

First, find the slope of the line on the graph:

m = \frac{y_2 - y_1}{x_2 - x_1}

Use the coordinates of any two points on the line. Let's use (-4, 0) and (0, -2)

m = \frac{-2 - 0}{0 -(-4)} = \frac{-2}{4} = -\frac{1}{2}

Slope of the line on the graph is -½.

Check each given line equation, ensure they are in the slope-intercept form and find out if the value of their slope is the same as -½.

Slope-intercept form is given as y = mx + b, where, m = slope.

Option 1: y = -½x

The slope of this line is -½, therefore it is parallel to the line on the graph.

Option 2: y = -½x + 3

The slope of this line is also -½, therefore it is parallel to the line on the graph.

Option 3: 2y = -x - 4

Rewrite in slope-intercept form.

y = -x/2 - 4/2

y = -½x - 2

The slope of this line is -½, therefore it is parallel to the line on the graph.

Option 4: y = 2x - 5.

The slope of this line is 2, therefore it is NOT parallel to the line on the graph.

Option 5: x + 2y = 8

Rewrite in slope-intercept form.

2y = 8 - x

y = 8/2 - x/2

y = 4 - ½x

The slope of this line is -½, therefore it is parallel to the line on the graph.

3 0
3 years ago
Help asap please, im timed
DochEvi [55]

Answer:

d

Step-by-step explanation:

3 0
3 years ago
For a field trip, a highschool want to buy T-shirts and sweatshirts. The expression px + 29y repersents the cost of buying x T-s
marysya [2.9K]

Answer:

The value of p is $12.

Step-by-step explanation:

Given;

c = px + 29y ,,,,,,,,,,,,,,,,,,, (1)

Where;

c = cost of buying x T-shirts and y sweatshirts from the store

p = price of one or each T-shirt = ?

x = number of T-shirts bought

29 = price of one or each sweatshirt

y = number of sweatshirt bought

Based on the above breakdown, if each sweatshirt cost $17 more than a T-shirt, the value of p can be calculated as follows:

29 = p + 17

p = 29 - 17

p = 12

Therefore, the value of p is $12.

Additional note:

Note that this is not part of the question but it is just an example to make you understand the question better.

If we assume that 10 T-shirts and 10 sweatshirts are bought from the store, we can use equation (1) above to calculate the cost as follows:

Where;

c = cost of buying x T-shirts and y sweatshirts from the store = ?

p = price of one or each T-shirt = 12

x = number of T-shirts bought = 10

29 = price of one or each sweatshirt

y = number of sweatshirt bought = 10

Substituting the values into equation (1), we have:

c = (12 * 10) + (29 * 10)

c = 120 + 290

c = 410

Therefore, the cost of of buying 10 T-shirts and 10 sweatshirts from the store will be $410.

5 0
3 years ago
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