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You want to solve a system of two equations in two unknowns
3x + 5y = 54 (1)
6x + 4y = 72 (2)
Divide second equation by 2 (both sides). Keep equation (1) as is.
You will get
3x + 5y = 54 (1)
3x + 2y = 36 (2')
Now subtract equarion (2') from equation (1).
The terms with "x" will cancel each other, since they have equal coefficients.
You will get
5y - 2y = 54 - 36
3y = 18
y = 18/3 = 6.
To find x, substitute y= 6 into equation (1). You will get
3x + 4*6 = 54 ---> 3x = 54 - 30 = 24 ---> x = 24/3 = 8.
ANSWER. x= 8, y= 6.
CHECK. To check, substitute the found values into given equations;
calculate left sides and compare with right sides.
Solved.
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It looks like you need to learn (to get familiar with) the general theory/technique on solving systems of two equations in two unknown.
In this site I developed such lessons for beginner students. These lessons are
- 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
Consider these lessons as your textbook, your handbook, your guide and your (free of charge) home teacher.
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".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.