Consider the following pair of equations: y = −2x + 8
y = x − 1

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answers

Answer 1

Answer: okay so you use the bottom to substitute y so your equation will be:
x-1=2x+8 now solve for x
-x-8=-x-8 this is what you will be taking away from both sides
-1-8=2x-x this is your new equation now you just do basic math
-9=x this is x
Now that you found x find y by substituting x
y=2(-9)+8
y= -18+8
y= (-10) this is your y
Now to check your answer on the other equation
y= -9-1
y= (-10) this is now correct
(x,y)form is (-9,-10)
Hopefully i helped out

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Multiply 3/sqrt17- sqrt2 by which fraction will produce an equivalent fraction with rational denominator

Answers

For this case we have the following expression:

$\frac {3} {\sqrt {17} - \sqrt {2}}$

We must rationalize the expression, so we multiply by:

$\frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}}$

So, we have:

$\frac {3} {\sqrt {17} - \sqrt {2}} * \frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}} =\n\frac {3 (\sqrt {17} + \sqrt {2}} {17- \sqrt {17} * \sqrt {2} + \sqrt {17} * \sqrt {2} -2} =\n\frac {3 (\sqrt {17} + \sqrt {2}} {15}$

Thus, the correct option is option B.

Answer:

OPTION B

Answer:

Step-by-step explanation:

To simplify something that looks like $\frac{\text{whatever}}{√(a)-√(b)}$ you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:

$√(a)+√(b)$ .

If you had $\frac{\text{whatever}}{√(a)+√(b)}$ , then you would multiply top and bottom the conjugate of $√(a)+√(b)$ which is $√(a)-√(b)$ .

The conjugate of a+b is a-b.

These have a term for it because when you multiply them something special happens. The middle terms cancel so you only have to really multiply the first terms and the last terms.

Let's see:

(a+b)(a-b)

I'm going to use foil:

First: a(a)=a^2

Outer: a(-b)=-ab

Inner: b(a)=ab

Last: b(-b)=-b^2

--------------------------Adding.

a^2-b^2

See -ab+ab canceled so all you had to do was the "first" and "last" of foil.

This would get rid of square roots if a and b had them because they are being squared.

Anyways the conjugate of $√(17)-√(2)$ is

$√(17)+√(2)$ .

This is the thing we are multiplying and top and bottom.

What is 10 = -9/2x - 7 - 3/2x
A = -17/6
B = -1/2
C = 17
D = 17/6

Answers

Answer:

x= -17/6

Step-by-step explanation:

10=-9/2x-7-3/2x

multiply all by 2

20=-9x-14-3x

add -9x to -3x

20=-12x-14

replace 20 with -12x and put -12x as a positive

12x=-14-20

add -14 to -20

12x=-34

divide both sides by 12

x= -17/6

Use algebra tiles to solve

Answers

Answer:

x=6

Step-by-step explanation:

-2x-3=-15

add 3 on both sides

-2x=-12

divide -2 on both sides

x=6

Answer:

x= 6

Step-by-step explanation:

Wats the 60% off a prize that is $20.00

Answers

$x\ \rightarrow\ the\ 60\%\ of\ a\ prize\ that\ is\ \$20.00\n\nx=60\%\ \cdot \ \$20.00= (60)/(100) \cdot \$20.00=\$12.00\n\nAns.\ \$12.00$

Benny bought 8 new baseball cards to add to his collection. The next day his dog ate half his collection. There are now only 36 cards left. How many did he start with? Answer in equation