Question 1085620
.
solve simultaneous equations algebraically
2y+x=9
3y-5x=20
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<pre>
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 = {{{65/13}}} = 5.

Then from the equation (1) x = 9 - 2y = 9 - 2*5 = 9 - 10 = -1.


<U>Answer</U>.  x= -1, y=5.
</pre>

Solved.


The method I applied is called "the Elimination method".



On solving systems of two linear equations in two unknowns see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-system-of-two-eqns-by-the-Subst-method.lesson>Solution of the linear system of two equations in two unknowns by the Substitution method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-Elimination-method.lesson>Solution of the linear system of two equations in two unknowns by the Elimination method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-using-det.lesson>Solution of the linear system of two equations in two unknowns using determinant</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of the linear system of two equations in two unknowns</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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