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solve simultaneous equations algebraically
2y+x=9
3y-5x=20
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2y + x = 9, (1)
3y - 5x = 20. (2)
Multiply equation (1) by 5 (both sides). You will get an equivalent system
10y + 5x = 45, (3)
3y - 5x = 20. (4)
Add the equations (3) and (4). The terms with "x" will cancel, and you will get
13y = 45 + 20 = 65, ----> y = = 5.
Then from the equation (1) x = 9 - 2y = 9 - 2*5 = 9 - 10 = -1.
Answer. x= -1, y=5.
Solved.
The method I applied 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".