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Can you please help me. I'm want to solve this system of equation using the substitution method.
-3x+3y=4
-x+y=3
~~~~~~~~~~~~~~~
-3x + 3y = 4, (1)
-x + y = 3 (2)
From (2), express y = 3+x and substitute this expression into equation (1) replacing y. You will get
-3x + 3(3+x) = 4.
Simplify:
-3x + 9 + 3x = 4.
9 = 4.
Absurd ? Sure. It means that the original system has no solutions.
It is inconsistent.
One can see it immediately/instantly after seeing the original system.
Indeed, multiply the second equation by 3.
You will get an equivalent equation
-3x + 3y = 9. (2')
Now compare (2') with (1). They have identical left sides, but different right sides.
Such a system is inconsistent.
For better understanding, 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 using determinant
- Solution of the linear system of two equations in two unknowns by the Elimination method
- 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".