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3 years ago

Solve the system by substitution 5x+y=-14 5x- 3y=2

Mathematics

1 answer:

dlinn [17]3 years ago

8 0

Answer:

x = -2, y = -4, or (-2, -4).

Step-by-step explanation:

5x + y = -14

5x - 3y = 2

If we look at the first equation, we can see that y can be easily isolated.

5x + y = -14

Subtract 5x from both sides.

y = -5x - 14

Now we have a variable that we can plug into the second equation.

5x - 3y = 2

5x - 3(-5x - 14) = 2

Distribute the -3 across each term in the parentheses.

5x + 15x + 42 = 2

Combine like terms.

20x + 42 = 2

Subtract 42 from both sides.

20x = -40

Divide both sides by 20 to isolate x.

x = -2

Plug in x = -2 back into one of the equations to find y.

y = -5x - 14

y = -5(-2) - 14

Multiply.

y = 10 - 14

Subtract.

y = -4

Our solution is x = -2, y = -4, or (-2, -4).

Check your answer by plugging both values into one of the equations.

5x - 3y = 2

5(-2) - 3(-4) = 2

-10 + 12 = 2

2 = 2

Your answer is correct.

Hope this helps!

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3 years ago

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Could someone help me with B

pishuonlain [190]

Answer:

$a_n = 12 - 3n$

Step-by-step explanation:

The first term is 9.

Term 1 is 9.

Term 2 is 9 - 3.

Term 3 is 9 - 2(3).

Term 4 is 9 - 3(3).

Term 5 is 9 - 4(5)

Notice the pattern in terms 3 through 5. For each term, subtract 1 less than the term number multiplied by 3 from 9.

For term n, you subtract 1 less than n times 3 from 9.

The nth term is 9 - (n - 1) * 3

$a_n = 9 - (n - 1) \times 3$

Now we simplify the expression on the right side.

$a_n = 9 - 3(n - 1)$

$a_n = 9 - 3n + 3$

The expression for the nth term is

$a_n = 12 - 3n$

Let's see if it works.

n = 1

$a_n = 12 - 3(1) = 12 - 3 = 9$

n = 2

$a_n = 12 - 3(2) = 12 - 6 = 6$

n = 3

$a_n = 12 - 3(3) = 12 - 9 = 3$

n = 4

$a_n = 12 - 3(4) = 12 - 12 = 0$

n = 5

$a_n = 12 - 3(5) = 12 - 15 = -3$

n = 6

$a_n = 12 - 3(6) = 12 - 18 = -6$

As you can see, following this rule fro the nth term, we got the same first siz terms you got above. Our answer is correct.

Answer: $a_n = 12 - 3n$

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