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3 years ago

Find the solution to the system of equations. y= 2x + 3 y= -3x + 3

Mathematics

1 answer:

Alexxandr [17]3 years ago

3 0

Answer:

(0, 3 )

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

y = - 3x + 3 → (2)

Since both equations express y in terms of x we can equate them, that is

2x + 3 = - 3x + 3 ( add 3x to both sides )

5x + 3 = 3 ( subtract 3 from both sides )

5x = 0 ⇒ x = 0

Substitute x = 0 into (1)

y = 0 + 3 = 3

Solution is (0, 3 )

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4.) Select ALL equivalent expressions to 5x – 5.5. a) 5x -55 c) 5(x - 1.1) b) 2x - 3 + 3x - 2.5 ) 5.5(x - 1)

lara [203]

Answer:

1. (-125 a - 5.75) x + b c (605 x - 550 x^2) + 10.75

2. -125 a x + x (-550 b c x + 605 b c - 5.75) + 10.75

3. 0.25 (-500 a x - 220 b c (10 x - 11) x - 23 x + 43)

Step-by-step explanation:

4 0

3 years ago

Gina Chuez has considered starting her own custom greeting card business. With an initial start up cost of $1500, she figures it

Digiron [165]

1.70 - 0.45 = 1.25

1500 ÷ 1.25 = 1200

Gina must sell 1200 cards before she can make a profit

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3 years ago

A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that

Igoryamba

Answer:

w =< 70

(width is less or equal to 70 inches)

Step-by-step explanation:

Let l = length, w = width, h = height

Restrictions given in this question:

'sum of perimeter of the base and the height cannot exceed 130 inches'

perimeter of the base is 2 width and 2 length of the box

perimeter = 2w + 2l

Therefore, inequality involves here is

2w + 2l + h =< 130

(Note that =< here means less or equal)

Then a new condition given with

height, h = 60 in

and length is 2.5 times the width

l = 2.5w

Substitute this new condition into the equation will give us the following:

2w + 2(2.5w) + 60 =< 130

2w + 5w + 60 =< 130

7w + 60 =< 130

7w =< 130-60

7w =< 70

w =< 10

4 0

3 years ago

7 + 79x79x= − 42 Solve this within 5 minutes !

Westkost [7]

42 rhhrhjejrjfitkkrjrjrhrt

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3 years ago

A business executive bought 40 stamps for

alekssr [168]

Answer:

32 33-cent stamps, 8 23-cent stamps

Step-by-step explanation:

In order to solve this question, we need to set up a system of equations. Also known as solving for two variables (the number of each stamp).

Let's set x to be the number of 33-cent stamps. Similarly, let's set y to be the number of 23-cent stamps.

To make our first equation, let's think about the number of stamps total we have. We can say:

$x + y =40$

<em>(AKA - The number of 33-cent stamps, plus the number of 23-cent stamps, equals 40 stamps.)</em>

Now, let's make an equation for the cost of these stamps.

$0.33x + 0.23y = 12.40$

<em>(AKA - The cost of the stamps in total, should equal $12.40).</em>

So now, we have our two equations:

$x + y =40\\0.33x+0.23y=12.40$

If you have a TI-84 graphing calculator, you can go to apps -> polysmlt2 -> simultaneous eqn solver, and then input these equations into the menu. This will solve the problem for you.

If you need to do this manually, let's use substitution. Condense our first equation to make it more substitutable.

$x+y=40\\x=40-y$

Now, let's put this into our second equation.

$0.33x+0.23y=12.40\\0.33(40-y)+0.23y=12.40$

Distribute, and solve for y.

$13.2-0.33y +0.23y =12.40\\13.2-0.1y=12.40\\-0.1y=-0.8\\y=8$

Now, we plug this into one of our equations.

$x+y=40\\x+8=40\\x=32$

In the end, we have thirty-two 33-cent stamps, and eight 23-cent stamps.

3 0

1 year ago