SOLUTION: solve simultaneous equations algebraically 3x+y=3 2x-y=7

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Question 1085622: solve simultaneous equations algebraically
3x+y=3
2x-y=7
Found 3 solutions by ikleyn, rothauserc, MathTherapy:
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve simultaneous equations algebraically
3x+y=3
2x-y=7
~~~~~~~~~~~~~~~~~ 

3x + y = 3,   (1)
2x - y = 7.   (2)

Add the two equations (both sides). You will get

5x = 3 + 7 = 10  --->  x = 10%2F5 = 2.

Then from equation (1) y = 3 - 3x = 3 - 3*2 = 3 - 6 = -3.


Answer.  x= 2,  y= -3.

This method is called "the Elimination method".


On solving systems of two linear equations in two unknowns see the lessons
    - Solution of the linear system of two equations in two unknowns by the Substitution method
    - Solution of the linear system of two equations in two unknowns by the Elimination method
    - Solution of the linear system of two equations in two unknowns using determinant
    - Geometric interpretation of the linear system of two equations in two unknowns
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".



Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) 3x + y = 3
2) 2x - y = 7
:
solve equation 1 for y
:
y = 3 - 3x
:
substitute for y in equation 2
:
2x - (3 - 3x) = 7
:
2x -3 + 3x = 7
:
5x = 10
:
x = 2
y = 3 - 3x = 3 - 3(2) = -3
:
**************************************************************
x = 2 and y = -3
:
check answers by substituting for x and y in equations 1 and 2
:
1) 3(2) + (-3) = 3
3 = 3
:
2) 2(2) - (-3) = 7
7 = 7
:
our answers check
**************************************************************
:

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve simultaneous equations algebraically
3x+y=3
2x-y=7
The easiest method to use is ELIMINATION.

You start by JUST ADDING the 2 equations to ELIMINATE y and get the value of x.

Substitute the value of x into any of the 2 original equations to get the value of y.

That's all. 



IGNORE anyone who tells you to solve this a different way, because from what is stated, 

this can be solved using any ALGEBRAIC method, and the easiest, least time-consuming is the ELIMINATION method.