Question 1144628
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<pre>
Without any explanations, it is clear that from the condition you have these 2 equations in 2 unknowns


    6x + 5y = 145   kilograms     (1)

    2x + 3y =  57   kilograms     (2)


To solve it, use Elimination method.

For it, multiply equation (2) by 3 (both sides).  Keep equation (1) as is


    6x + 5y = 145                 (1')

    6x + 9y = 171                 (2')


From equation (2') subract equation (1').  The terms  " 6x " will cancel each other, and

you will get one single equation for "y"


    9y - 5y = 171 - 145,   or

    4y       = 26

     y       = 26/4 = 6.5.


Thus small box weights 6.5 kilograms.

Now substitute it into equation (2) to find "x" :


    2x + 3*6.5 = 57,

    2x = 57 - 3*65 = 37.5.

     x             = 37.5/2 = 18.75.


<U>ANSWER</U>.  Large box weights  18.75 kilograms.  Small box weights  6.5 kilograms.


<U>CHECK</U>.  Equation (1) :  6*18.75 + 5*6.5 = 145 kilograms.   ! Correct !

        Equation (2) :  2*18.75 + 3*6.5 = 57 kilograms.   ! Correct !
</pre>

Solved.


On the way, you learned on how the Elimination method works.


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.
On solving systems of 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 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=https://www.algebra.com/algebra/homework/coordinate/lessons/Useful-tricks-when-solving-systems-of-2-eqns-in-2-unknowns-by-the-Subst-method.lesson>Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method</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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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Roses-and-violets.lesson>Roses and vilolets</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/Counting-calories-and-grams-of-fat-in-combined-food.lesson>Counting calories and grams of fat in combined food</A>

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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/How-to-algebreze-and-to-solve-this-problem-on-2-eqns-in-2-unknwns.lesson>HOW TO algebreze and solve this problem on 2 equations in 2 unknowns</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/One-unusual-problem-to-solve-using-system-of-two-equations.lesson>One unusual problem to solve using system of two equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Solving-mentally-word-problems-on-two-equations-in-two-unknowns-NEW.lesson>Solving mentally word problems on two equations in two unknowns</A> 

in this site. They all are free of charge.


Also, &nbsp;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>".



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.