All categories

3 years ago

Solve the system by substitution. 4x=8y 2x+5y=27

Mathematics

2 answers:

MAVERICK [17]3 years ago

3 0

Answer:

(6, 3)

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Alg I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define systems

4x = 8y

2x + 5y = 27

Step 2: Rewrite systems

x = 2y

2x + 5y = 27

Step 3: Solve for y

Substitute: 2(2y) + 5y = 27
Multiply: 4y + 5y = 27
Combine like terms: 9y = 27
Isolate y: y = 3

Step 4: Solve for x

Plug in y into an original equation to find x.

Substitute: 4x = 8(3)
Multiply: 4x = 24
Isolate x: x = 6

Alex777 [14]3 years ago

3 0

Answer:

$(6,3)$

Step-by-step explanation:

$4x = 8y\\4x/4 = x\\8y/4= 2y\\x=2y$

$2(2y)+5y=27\\4y+5y=27\\9y=27\\9y/9=y\\27/9=3\\y=3$

$x =2y\\x= 2(3)\\x=6$

You might be interested in

The exchange rate is: £1 = €1.12. How much £ would I get for €336

SVETLANKA909090 [29]

£1 = € 1.12
£ x = € 336

Create proportions
Cross multiply
Divide
You will eventually find the answer

Proportions
$\frac{1}{1.12} = \frac{x}{336}$

cross multiply
336 = 1.12x

Divide to isolate x
$\frac{336}{1.12} = \frac{1.12x}{1.12}$
1.12 and 1.12 cancels out

300 = x

£300 = €336

8 0

3 years ago

Please help me with this

Wewaii [24]

300 ft jdndjdjdjdnnsbshshdbdbbdbdhd

7 0

3 years ago

Read 2 more answers

The function that passes through thepoints (24, 28) and (8,8)Is?

icang [17]

The slope of the line that passes through the points (x1, y1) and (x2,y2) is computed as follows:

$m=\frac{y_2-y_1}{x_2-x_1}$

In this case, the points are (24, 28) and (8,8), then its slope is:

$m=\frac{8-28}{8-24}=\frac{-20}{-16}=\frac{5}{4}$

The slope-intercept form of a line is:

y = mx + b

where m is the slope and b is the y-intercept

Substituting into the general equation with m = 5/4 and the point (24, 28) we get:

$\begin{gathered} 28=\frac{5}{4}\cdot24+b \\ 28=30+b \\ 28-30=b \\ -2=b \end{gathered}$

Finally, the equation is

y = 5/4x - 2

3 0

1 year ago

The width of a rectangle is 6 cm less than its length. If its perimeter is 80 cm then its lengths (in cm) and area (in cm²) are

mr_godi [17]

Start by stating the given info as mathematical expressions:

1. "The width of a rectangle is 6 cm less than its length."
$w=l-6$

2. "Its perimeter is 80 cm."
$P=80$

Using the formula for perimeter ( $P=2l+2w$ ) we can show:
$80=2l+2w$ .

We now have 2 equations in 2 unknowns and can solve by substitution:
 $80=2l+2w$
$80=2l+2(l-6)$
$80=2l+2l-12)$
$92=4l$
$l=23$

The length is 23cm.

Having the length w can then find the width:
$w=l-6$
$w=23-6$
$w=17$

The width is 17cm.

And finally the area:
$A=lw$
$A=(23)(17)$
$A=391$

The area is $391cm^{2}$ .

As a check we can use the known perimeter:
$80=2l+2w$
$80=2(23)+2(17)$
$80=46+34$
$80=80$ Checks true.

5 0

4 years ago

A private plane can hold 14 students. If there are 2,147 students going on a trip, how many private planes will need to be used

djyliett [7]

Answer:153.357

Step-by-step explanation:

8 0

3 years ago