SOLUTION: Solve using any method: Substitution or Addition Method or Elimination Method y = 2x

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Question 1203967: Solve using any method: Substitution or Addition Method or Elimination Method

y = 2x - 3
-6x + 3y = -9
Found 3 solutions by MathLover1, josgarithmetic, greenestamps:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

....eq.1
.....eq.2
_________________________________
using substitution
.....eq.2, substitute from eq.1

it means we have two lines on top of each other, or same line
let's check eq.2, solve for
.....eq.2
.....both sides divide by
which is same as eq.1

Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
-----------------------
y = 2x - 3
-6x + 3y = -9
----------------------

Second equation,

Substituting according to the first equation: ;
, which is true and the variables are lost.

LOOK at the system carefully!

-
---------the two equations are equivalent. All points on the one line are solutions.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

The two responses you have received showing a solution using substitution are valid.

I would change the form of the second equation, after which a solution by either substitution or elimination is obvious.

(1) y = 2x-3
(2) -6x+3y = -9 --> 3y = 6x-9 --> y = 2x-3

We see the two equations are equivalent, so the solution is all the sets of ordered pairs that satisfy the equation.

Finishing the problem formally using substitution, we would have

2x-3 = 2x-3
2x-2x = 3-3
0 = 0

Which is always true...

or by elimination

y = 2x-3
y = 2x-3
0 = 0 (by subtraction)

which again is always true.

SOLUTION: Solve using any method: Substitution or Addition Method or Elimination Method y = 2x - 3 -6x + 3y = -9