What is the system of quations??

Question

What is the system of equations for these two and how do you find it?:

y=x-3 and y=2x-5

Also these two?:

2x+y=-1 and y=-3

Thank you!

Answer 1

If y=x+3, then:

STEP 1:  substitute 'x+3' into the second equation, like this:

x+3=2x-5

STEP 2:  solve for x:

-x+x+3=2x-5-x

3=x-5

5+3=x-5+5

8=x

STEP 3:

Substitute the value for x (8) into the equation and solve for y:

y=8-3

y=5

Check:

5=8-3 - a true statement, so we've found the answer.

Ordered pair:

(8,5)

For the second system, if y=-3, then 

STEP 1 substitute -3 for y and solve for x

2x+(-3)=-1 

2x-3+3=-1+3

2x=2

x=1

Your ordered pair is (1,-3)

Answer 2

The system consists of the equations in standard form, which the second set of equations is already in since all the terms that have a variable (x or y) associated with them are on one side of the equation and all other term(s) are on the other side of the equation. 

For the first set of equations, simply rearrange the terms in such a way that will have all terms with a variable on one side and all other terms on the other side of the equation. That is,

     y = x - 3          subtract x from both sides of the equation

     -x + y = -3   ==>   by changing the signs of all the terms you get:    x - y = 3

and

     y = 2x - 5          subtract 2x from both sides of the equation

     -2x + y = -5   , by changing the signs of all the terms you get:   2x - y = 5 

So the system of equations is:     x - y = 3     and     2x - y = 5