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24x+2y=52 6x+3y=-36
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24x + 2y = 52 (1)
6x + 3y = -36 (2)
Divide the first equation by 2 (both sides).
Divide the second equation by 3 (both sides). You will get an equivalent system
12x + y = 26 (1')
2x + y = -12 (2')
Now distract the second equation from the first one.
In this way you eliminate "y" and get a single equation for x:
12x - 2x = 26 - (-12),
10x = 26 + 12 = 38 ---> x = = 3.8.
Next, from (2') y = -12 - 2*3.8 = -19.6.
Answer. x = 3.8, y = -19.6.
The method I applied here is called the Elimination method.
On the Substitution method, Elimination method, Determinants' method for solving the systems of two linear equations
in two unknowns see the lessons
- 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 Substitution method
- 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".