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3 years ago

A system of equations has infinitely many solutions. If 2y - 4x = 6 is one of the equations, which could be the other

Mathematics

2 answers:

stira [4]3 years ago

8 0

Answer:

C. –y = –2x – 3

Step-by-step explanation:

edg. unit test

Serjik [45]3 years ago

6 0

Answer:

-y = -2x - 3

Option 3

Step-by-step explanation:

When equations are equivalent, they will have infinitely many solutions.

If you want to find an equivalent equation, you can multiply/divide every term in the equation by the same number. You can also rearrange the equation.

Since the options mostly have "y" by itself, start by rearranging to isolate "y" in the given equation.

Move all the other numbers to the right of the equal sign except for "y". To move a number, apply its reverse operation to the entire equation.

Do reverse operations in reverse BEDMAS order.

2y - 4x = 6 Move "-4x" first. It's reverse is +4x.

2y - 4x + 4x = 6 + 4x

2y = 6 + 4x Move the "2" in 2y. Divide the whole equation by 2.

2y/2 = 6/2 + 4x/2

y = 3 + 2x Rearrange to look like the answer choices.

y = 2x + 3

This equation looks like option 3 except every term has a different negative/positive.

y = 2x + 3 -y = -2x - 3

We can multiply every term by -1.

y = 2x + 3

y*-1 = 2x*-1 + 3*-1

-y = -2x + (-3) Negative and positive make a negative

-y = -2x - 3 Same as option 3

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Kristen invests $5,745 in a bank. The bank pays 6.5% interest compounded monthly. How long must she leave the money in the bank

s344n2d4d5 [400]

formula is $A=P(1-\frac{r}{n})^{nt}$

where A=final amount

P=principal

r=interest rate in decimal

n=number of times per year it is compounded

t=time in years

we want to find where

A=2P

and P=5745

and r=6.5%=0.065

n=monthly=12

remember that $ln(x^a)=a(ln(x))$

also that $(a^b)^c=a^{bc}$

$2(5745)=5745(1+\frac{0.065}{12})^{12t}$ , solving for t

divide both sides by 5745 to simplify things a bit

$2=(1+\frac{0.065}{12})^{12t}$ I'd rather not simplify this because it give us a decimals and those aren't exact, if we combine, we get 12.065/12 for inside parenthases