Y=6x, 2x+3y=-20
Substitution means just plugging in another equation equal to a single variable in order to solve for the other variable, and then the first. In this case, the equation being plugged in is y=6x, so 6x will be put in place of y in the equation 2x+3y=-20.
2x+3(6x)=-20
2x+18x=-20
20x=-20
x=-1
And then x=-1 can be plugged into the original equation to find y. (And, if you wish, into the y= equation to check it.)
2(-1)+3y=-20
-2+3y=-20
3y=-20+2
3y=-18
y=-6
And to check it, we plug the two into the original y= equation.
y=6x
-6=6(-1)
-6=-6
They are equal, so both check out.
x=-1, y=-6

7 0

3 years ago

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Find the points of intersection of the lines 10x−4y=2 and 2x+8y=7 without graphing.

Jet001 [13]

Answer:

$x=\frac{1}{2},y=\frac{3}{4}$

Step-by-step explanation:

Given:

$10x-4y=2 ,2x+8y=7$

To find: points of intersection of the given lines

Solution:

In substitution method, the system of equations is solved by expressing one variable in terms of another, as a result, removing one variable from an equation.

$10x-4y=2 \\2(5x-2y)=2\\5x-2y=1\\5x=1+2y\\x=\frac{1+2y}{5}$

Put $x=\frac{1+2y}{5}$ in the equation $2x+8y=7$

$2x+8y=7\\2[\frac{1+2y}{5}]+8y=7\\ 2+4y+40y=35\\44y=35-2\\44y=33\\y=\frac{33}{44}\\ =\frac{3}{4}$

Put $y=\frac{3}{4}$ in the equation $x=\frac{1+2y}{5}$

$x=\frac{1+2y}{5}\\=\frac{1}{5}[1+2(\frac{3}{4})]\\=\frac{1}{5}[1+(\frac{3}{2})]\\\\=\frac{1}{5}(\frac{2+3}{2}) \\\\=\frac{1}{5}(\frac{5}{2})\\\\=\frac{1}{2}$

Therefore,

$x=\frac{1}{2},y=\frac{3}{4}$

5 0

3 years ago

If 24 water bottles weigh 30 pounds, how much would a shipment of 150 water bottles weigh?

mojhsa [17]

Answer:

A shipment of 150 bottles will weigh 120 pounds.

Step-by-step explanation:

Given that:

24 bottles of water weigh 30 pounds

Ratio of bottles to weight = 24 : 30

Number of bottles in shipment = 150

Weight of bottles = x

Ratio = x : 150

As the relation is proportional

24 : 30 :: x : 150

Product of mean = Product of extreme

30x = 24 * 150

30x = 3600

Dividing both sides by 30

$\frac{30x}{30}=\frac{3600}{30}\\x= 120$

Hence,

A shipment of 150 bottles will weigh 120 pounds.

4 0

3 years ago