Question

...

Answer 1

Your school class is taking a trip.

There are two chaperons to every boy x and one chaperon to every girl y. The total number of chaperons is ten.
2x + y = 10

Each boy x has three dollars to spend for lunch, while each girl y has four dollars to spend for lunch. Together, boys and girls brought twenty-five dollars to pay for lunch.
3x + 4y = 25

How many boys and girls are on the trip?

Answer 2

I think this should work, you can check. Also, you can solve for boys x and girls y.

Answer 3

Yes, I do.

Answer 4

Are you familiar with the methods available to us for solving a system of equation?

substitution

and

elimination

??

Answer 5

If not we are trying to read without knowing the alphabet.

Answer 6

primer to solving systems of equations: read this then we can proceed

http://tutorial.math.lamar.edu/Classes/Alg/SystemsTwoVrble.aspx

Answer 7

once you read the material, let me know if you want to use substitution of elimination and we can solve this together

Answer 8

2x + y = 10
3x + 4y = 25

are we eliminatin the x or the y variable

Answer 9

ok so right now 4y - y = 3y, that will not eliminate the variable, we need to subtract 4y and 4y to get rid of it to 0

so

by what factor do we need to augment the fjirst system to obtain 4y - 4y

Answer 10

2x + y = 10
3x + 4y = 25
.subtraction
-x - 3y = -15

See how this does not eliminate our variable y? we need to scale the first equation to make it so it eliminates properly

Answer 11

1 * (2x + y = 10)

1*2x + 1*y = 1*10

2x + y = 10

It does not help us much to multiply by 1

Answer 12

-4 * (2x + y = 10)

-4*2x + -4*y = -4*10

-8x - 4y = -40

Answer 13

Now we are looking at

-8x - 4y = -40
3x + 4y = 25

Answer 14

This is beginning to look nice isnt it

Answer 15

-8x - 4y = -40
3x + 4y = 25
.addition
-5x + 0 = -15

-5x = -15
.solve

x = 3

Answer 16

Be careful of your signs.

x = 3.

Now that we know x, we can plug x back in to EITHER equation and obtain a y value.

What do you obtain for y

Answer 17

2x + y = 10

x = 3

2(3) + y = 10

6 + y = 10

y = 10 - 6

y = 4

Answer 18

You can never be too sure in math. Let us super check.

2x + y = 10
3x + 4y = 25

x = 3, y = 4

2x + y = 10
2(3) + (4) = 10
6 + 4 = 10
10 = 10
checks

3x + 4y = 25
3(3) + 4(4) = 25
9 + 15 = 25
25 = 25
checks

And you are now familiar with elimination method

Answer 19

When I first saw this system, I wanted to use substitution because I saw that 2x + y = 10 easily set me up to say y = 10 - 2x

2x + y = 10

or
y = 10 - 2x
3x + 4y = 25

3x + 4(10 - 2x) = 25

3x + 40 - 8x = 25
15 = 5x
x = 3

Plug back in to y = 10 - 2x
y = 10 - 2(3)
y = 10 - 6
y = 4