All categories

3 years ago

When using the substitution method what is the system of equations x+y=5 6x+3y=27

Mathematics

1 answer:

crimeas [40]3 years ago

8 0

9514 1404 393

Answer:

y = 5 -x

6x +3(5 -x) = 27

Step-by-step explanation:

The first equation is conveniently solved for either x or y. If we solve it for y, we get ...

y = 5 - x . . . . . . subtract x from both sides

This expression for y can be substituted into the second equation to give ...

6x +3(5 -x) = 27

These are your new system of equations.

Simplified, they are ...

y = 5 -x
3x +15 = 27

_____

The second is a 2-step equation that gives the value of x, which can then be used in the first equation to find y.

3x = 12 . . . . subtract 15

x = 4 . . . . . . divide by 3

y = 5 -4 = 1 . . . . substitute into the first equation

The solution is (x, y) = (4, 1).

You might be interested in

Solve for y 2x-3y=-9

labwork [276]

Answer:

y=3+2x/3

Step-by-step explanation:

− 3 y=− 9 − 2x

Divide each term by -3 and simplify.

7 0

3 years ago

Run 6.99999 to one decimal number

Black_prince [1.1K]

Answer:

*round - answer is 7

Step-by-step explanation:

anything 5 or greater rounds up, so 6 rounds up to 7 since 9 > 5

4 0

3 years ago

Read 2 more answers

What is the total repayment made, including principal and interest, on a loan of $1,100 at 3.5% interest compounded annually ove

olchik [2.2K]

The total repayment made, including principal and interest is $1262.27

<h3>Compound interest</h3>

The formula for calculating the compound interest is calculated as shown below;

A = P(1+r)^t

where

P is the principal = $1100

rate = 3.5% = 0.035

time "t" =4 years

Substitute

A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)

A = 1262.27

Hence the total repayment made, including principal and interest is $1262.27

learn more on compound interest here: brainly.com/question/24924853

#SPJ1

8 0

2 years ago

Peter read 24 pages of a book, and Chelsea read 1/3 as many pages of the same book. How many pages did Chelsea read?

bekas [8.4K]

Answer:

Step-by-step explanation:

1/3 of 24 is 8 i hope this helps

8 0

3 years ago

Read 2 more answers

What must be the sides of an equilateral triangle so that it's area should be equal to the area of an isosceles triangle with ba

d1i1m1o1n [39]

Answer:

The sides of the equilateral triangle are 11.7 m.

Step-by-step explanation:

Let's find the area of the isosceles triangle:

$A_{i} = \frac{bh}{2}$

Where:

b: is the base = 12 m

h: is the height

We can find the height by using Pitagoras:

$x^{2} = \frac{b^{2}}{2} + h^{2}$

Where:

x is the hypotenuse = side of the triangle = 10 m

$h = \sqrt{x^{2} - \frac{b^{2}}{2}} = \sqrt{(10)^{2} - 6^{2}} = 8 m$

Then, the area is:

$A_{i} = \frac{12*8}{2} = 48 m^{2}$

Now, since the area of the isosceles triangle is equal to the area of the equilateral triangle:

$A_{e} = A_{i} = 48 m^{2}$

$A_{e} = \frac{bh}{2}$

The height of the equilateral triangle is given by:

$b^{2} = \frac{b^{2}}{2} + h^{2}$

$h = \sqrt{b^{2} - \frac{b^{2}}{2}} = \frac{b}{\sqrt{2}}$

Hence, the sides are:

$A_{e} = \frac{1}{2}b\frac{b}{\sqrt{2}} = \frac{b^{2}}{2\sqrt{2}}$

$b = \sqrt{A*2\sqrt{2}} = \sqrt{48*2\sqrt{2}} = 11.7 m$

Therefore, the sides of the equilateral triangle are 11.7 m.

I hope it helps you!

7 0

3 years ago

Read 2 more answers

When using the substitution method what is the system of equations￼ x+y=5 6x+3y=27￼

When using the substitution method what is the system of equations x+y=5 6x+3y=27