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3 years ago

Match the system of equations on the left with the number of solutions on the right

Mathematics

1 answer:

erastova [34]3 years ago

6 0

Answer:

top to bottom, the answers are b, c, a

Step-by-step explanation:

One way to find the solution to a system of equations is to substitute values in. For the first one,

y=2x+3

y=2x+5,

we can substitute 2x+3 =y into the second equation to get

y=2x+5

2x+3 = 2x+5

subtract 2x from both sides

3 = 5

As 3 is not equal to 5, this is never equal and therefore has no solution

For the second one,

y= 2x+7

y = (-2/3)x + 10

We can plug y=2x+7 into the second equation to get

2x + 7 = y = (-2/3)x + 10

2x + 7 = (-2/3)x + 10

add (2/3)x to both sides to make all x values on one side

2x + (2/3)x + 7 = 10

subtract 7 from both sides to make only x values on one side and only constants on the other

2x + (2/3)x = 3

(6/3)x + (2/3)x = 3

(8/3)x = 3

multiply both sides by 3 to remove a denominator

8x = 9

divide both sides by 8 to isolate x

x=9/8

There is only one value for when the equations are equal, so this has one solution

For the third one

y = x-5

2y = 2x - 10

Plug x-5 = y into the second equation

2 * y= 2*(x-5)

2 * (x-5) = 2x - 10

2x-10 = 2x-10

add 10 to both sides

2x=2x

As 2x is always equal to 2x, no matter what x is, there are infinitely many solutions for this system

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$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year
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We know for our problem that $P=6200$ and $t=5$ . To convert the interest rate to decimal form, we are going to divide the rate by 100%:
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Since the type of the annuity is ordinary, payments are made at the end of each period, and we know that we have 2 periods, so $n=2$ .
Lets replace the values in our formula:

$FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]$
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