Question

Help! Totally confused on this:

What is the solution to the following system

3x + 3y = 10
-9x - 9y = -30

Answer 1

Are you sure you copied the equations correctly?

Answer 2

yes I checked it twice

Answer 3

i get 0 = 0 every time. whether I substitute or eliminate. Can we use matrices? Did you learn that yet?

Answer 4

I multiplied the top equation by 3 but that cancelled out x and y and I got totally confused.

Answer 5

I am learning matrices but still confused on how to do it

Answer 6

Lets do it that way.

you take each coefficient and create a matrix each equation has its own row

3 3 | 10
-9 -9 | -30

The goal is to get the top left number a 1 and then the principal diagonal (top left to bottom right) numbers all 1 with everything else 0.

Answer 7

You can add to rows together, multiply one row by a scalar then add, but you cannot multiply 2 rows together

Answer 8

ok. I kind of understand but still kinda confused

Answer 9

solve y or x

Answer 10

3 3 | 10
-9 -9 | -30 add (3 times row 1) to row 3

[The reason the top row stays the same is we assume after each operation we undo the operation to the row, this manipulates the row we want leaving the other unharmed]

3 3 | 10 divide row 1 by 3
0 0 | 0

1 1 | 10/3
0 0 | 0

Now we have a 1 in the top left spot. If we rewrite this equation we have

x + y = 10/3
the bottom equation is arbitrary. since y ( or the bottom right is a 0) we can say let y = s
where s is some number.

now the equations are
x + s = 10/3
y = s

Answer 11

now we can write the solution in matrix form as
| x | = s | -1 | + 10/3 | 1 |
| y | | 1 | | 0 |

Answer 12

Quick adjustment to previous post where I say **now the equations are**

They need to be written in terms of x and y so they are

x = -s + 10/3
y = s

Answer 13

oh ok That makes sense

Answer 14

What class is this for?

Answer 15

algebra 2

Answer 16

I can't remember what the answer would be in terms of what you have learned in algebra 2 but in my differential equations class the correct answer would the matrix form I posted

Answer 17

ok thank you for your help.

Answer 18

3x + 3y = 10
-9x - 9y = -30

this system is dependent...
mulitply the first equation by -3 and notice you'll get exactly the second equation...
this means they are the same lines....
which means there are infinitely many solutions....
every point on one line, is a point on the other....