All categories

3 years ago

Solve the system by substitution. y = -3x + 4 y = -7x Submit Answer

Mathematics

1 answer:

iVinArrow [24]3 years ago

5 0

Answer:

{y,x} = {7,-1}

Step-by-step explanation:

(-7x) + 3x = 4

- 4x = 4

4x = - 4

x = - 1

y = -7x

x = -1

y = -7(-1) = 7

You might be interested in

Help pleaseeeee it’s urgent!!!

Ad libitum [116K]

Answer:

(2,-7)

Step-by-step explanation:

Use the midpoint formula! (Attached is a picture of it!)

1) Plug in the values:

(5-1)/2,(-6+-8)/2

2) Simplify:

4/2,-14/2

3) Solve:

(2,-7)

6 0

4 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

How do you solve 32 - 6x = 53?

katrin2010 [14]

$\large\boxed{x=-\frac{7}{2}}$

To solve for $x$ , we need to isolate it on one side of the equation.

The most important part of this is knowing that whatever we do to one side of the equation, we must also do to the other.

Subtract 32 from both sides of the equation.

$\begin{aligned}32-32-6x&=53-32\\-6x&=21\end{aligned}$

Divide both sides of the equation by $-6$ .

$\begin{aligned}\frac{-6x}{-6}&=\frac{21}{-6}\\x&=\boxed{-\frac{7}{2}}\end{aligned}$

7 0

2 years ago

Read 2 more answers

.. Find the L.C.M. of (a - 5)(a – 4) and (a + 4)(a – 5)

andrew-mc [135]

A-5 A-5 AND A-4 A-5

A-10 AND A-1

Hope it helps you

3 0

3 years ago

Read 2 more answers

23. Which equation is equivalent to 3x+ 4y = 15?

Vlad [161]

Answer:

$y=\frac{15}{4}-\frac{3}{4}x$

Step-by-step explanation:

$3x+ 4y = 15\\4y=15-3x\\y=\frac{15}{4}-\frac{3}{4}x$

5 0

4 years ago