All categories

2 years ago

Solve the following system of equations by substation.

Mathematics

1 answer:

Cerrena [4.2K]2 years ago

7 0

Answer:

C. (-1, 3)

Step-by-step explanation:

Label the 2 equations:

5y= 7x +22 -----(1)

x= -6y +17 -----(2)

Substitute (2) into (1):

5y= 7(-6y +17) +22

5y= -42y +119 +22 (Expand bracket)

5y= -42y +141 (Simplify)

42y +5y= 141 (+42y on both sides)

47y= 141

y= 141 ÷47 (÷47 on both sides)

y= 3

Substitute y= 3 into (2):

x= -6(3) +17

x= -18 +17

x= -1

Thus, the solution is (-1, 3).

You might be interested in

Complete the steps to solve the polynomial equation x3 – 21x = –20. According to the rational root theorem, which number is a po

jeka94

Answer:

Zeroes : 1, 4 and -5.

Potential roots: $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

Step-by-step explanation:

The given equation is

$x^3-21x=-20$

It can be written as

$x^3+0x^2-21x+20=0$

Splitting the middle terms, we get

$x^3-x^2+x^2-x-20x+20=0$

$x^2(x-1)+x(x-1)-20(x-1)=0$

$(x-1)(x^2+x-20)=0$

Splitting the middle terms, we get

$(x-1)(x^2+5x-4x-20)=0$

$(x-1)(x(x+5)-4(x+5))=0$

$(x-1)(x+5)(x-4)=0$

Using zero product property, we get

$x-1=0\Rightarrow x=1$

$x-4=0\Rightarrow x=4$

$x+5=0\Rightarrow x=-5$

Therefore, the zeroes of the equation are 1, 4 and -5.

According to rational root theorem, the potential root of the polynomial are

$x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}$

Constant = 20

Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.

Leading coefficient= 1

Factors of leading coefficient ±1.

Therefore, the potential root of the polynomial are $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

3 0

3 years ago

You can buy 5 items for $10, how much will it cost for 8 items?

shtirl [24]

Answer:

$16

Step-by-step explanation:

Looking at the Price for 5 Items (10 dollars), That means the Price Per Item Is 2 dollars. Now we know the Cost per Item, We need to multiply the Cost per item by 8 (2*8) making it 16.

4 0

2 years ago

Read 2 more answers

Mr. Mika paid a total of $150 to rent a room at a hotel for two nights. The table shows information about four other

julia-pushkina [17]

Answer:

Well, one night at the hotel equals $75.

Step-by-step explanation:

All you have to do is mulitlpy the nights by $75.

The last one is wrong it should be

5 nights = $375.

Hope this helps! Bye

4 0

3 years ago

1. What decimal is equivalent to 23/100? plz explain :)

MAVERICK [17]

1] 0.23
2] both are same
3] 20/100 *80= 16

7 0

3 years ago

The volume of a suitcase is 4.2 cubic feet. what is the volume of a suitcase that is smaller by a factor of 0.9? round to the ne

ANEK [815]

The volume would be 0.9 x 4.2

This means it is 90% smaller

Don't forget to round the nearest tenth place. That's the first decimal, so you answer should only have 2 digits.

3 0

3 years ago