Question

to determine if an ordered pair is a solution to a system of linear equations in two variables

Answer 1

The simplest solution I can think of is just to place it in both equations and see if it fits:
In the ordered pair you have both let's say (x, y), so you can substitute it with the variables in those equations and see if it is a real equality for both

Answer 2

do you want an example or is that clear enough? o.o

Answer 3

K i'm back. so let's see.. an example I guess =]

Answer 4

let's take just 2 linear functions I just made up:
\[
x = y +6 \\
y = 3x + 2
\]
Now just give me a random point (x,y)

Answer 5

thats good enough. thanks.

Answer 6

In the system –12c + 3d = 6 and –3c + 6d = –9, which expression could you use for substitution?

Answer 7

Well, you asked to determine if an ordered pair is the solution of the system, so I gave the simplest way doing it.
If you don't have any ordered pair, and you want to find the solution that's a different case.
Is that what you need?

Answer 8

this is a different question.

Answer 9

\[
\left \{ \begin{array}{l l}
-12c + 3d = 6 \;// +12c \\
-3c + 6d = -9 \;// +3c
\end{array}
\right. \\

\left \{ \begin{array}{l l}
3d = 6 + 12c \;// \div 3\\
6d = -9 + 3c \;// \div 6
\end{array}
\right. \\

\left \{ \begin{array}{l l}
d = 2 + 4c \\
d = -\frac{3}{2} + \frac{c}{2} = \frac{c - 3}{2}
\end{array}
\right. \\
\]
Now since we know what d is in both equations, we can check for which 'c' values this is equal:
\[
2 + 4c = \frac{c - 3}{2} \;// \cdot 2 \\
4 + 8c = c - 3 \\
7c = -7 \\
c = -1
\]
Now finally since we know those 2 equations have the same spot at c=1, we want to find what is the d at that spot. we can use either one of the original equations:
\[
d = 2 + 4c \\
d = 2 + 4 \cdot (-1) = 2- 4 = -2
\]
so. c = -1, d = -2
last one, a check (which is what I meant above):
\[
-12c + 3d = 6 \implies -12 \cdot (-1) + 3 \cdot (-2) = 6 \implies \\
\implies 12 - 6 = 6 \implies 6=6\\ \;\\
-3c + 6d = -9 \implies -3 \cdot (-1) + 6 \cdot (-2) = -9 \implies \\
\implies 3 - 12 = -9 \implies -9 = -9
\]
So here, it's all good.

Answer 10

thanks i gave you a medal since you got it right.

Answer 11

I prefer a medal if you got my explanation, otherwise there is no really point heh..
I could just give you a solution, but I truly hope you would understand all those at the end and be able to solve them by yourself..

Answer 12

i got your explanation. how old are you? and are you a boy or girl/

Answer 13

What is the first step in solving the following system of equations by substitution?
9x-2=4y
x=6-y

Answer 14

sorry back. was in different question. reading

Answer 15

Well.. I'm a 20 years old (old...) boy.
And to the question
first step would be to get in both equations the same variable isolated.
I would go for the 'y' because it has smaller coefficient.
Can do?