Question 1041322
.
2x + 9y = 29
-5x + y = 45
~~~~~~~~~~~~~~~~~~~~~~~


<pre>
2x + 9y = 29,           (1)
-5x + y = 45            (2)

I will show you how to solve it by applying the Substitution method.

From the equation (2), express "y" via x  y = 45 + 5x. 
Next substitute this expression for "y" into equation (1). Then (1) takes the form

2x + 9*(45+5x) = 29.    (3)

Now simplify and solve it:

2x + 405 + 45x = 29  --->  47x = 29 - 405  --->  47x = -376  --->  x = {{{-376/47}}} = -8.

Thus we got x = -8.  Then from (2) y = 45 + 5x = 45 + 5*(-8) = 5.

Please check yourself the answer.

<U>Answer</U>.  x = -8, y = 5.
</pre>

On solution systems of two 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 a 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 a 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 a 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 a linear system of two equations in two unknowns</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solving-word-probs-using-linear-systems-of-two-eqns-with-two-unknowns.lesson>Solving word problems using linear systems of two equations in two unknowns</A> 

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