document.write( "Question 1135572: Hi, Denise here. nice to meet you. I am studying algebra and am having problems with the algebraic word problems. I need help with.\r
\n" ); document.write( "\n" ); document.write( "1.) Joshua paid $26.50 for 10 gallons of gas and 2 quarts of oil. Anthony paid $23.58 for 8 gallon of gas and 3 quarts of oil. Find the cost of 1 gallon of gas and 1 quart of oil.\r
\n" ); document.write( "\n" ); document.write( "now I guess my distinction is: Let x= 1 gallon of gas, Let y= 1 quart of oil
\n" ); document.write( "and the equations I made for Joshua's: 10x + 2y=26.50
\n" ); document.write( "and Anthony's: 8x + 3y=23.58\r
\n" ); document.write( "\n" ); document.write( "Is this right? and if so. this I can't figure out what to use the demonstation of substitution or addition?? please help me? Thanks. your prompt results are very appreciated.
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Algebra.Com's Answer #753200 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "From the condition, you have these two equations\r\n" );
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document.write( "   10x + 2y = 26.50    (1)\r\n" );
document.write( "    8x + 3y = 23.58    (2)\r\n" );
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document.write( "So, my equations and my variables are exactly as yours.\r\n" );
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document.write( "Now, if you try to apply the Substitution method directly as you learned it in the school, you will have denominators,\r\n" );
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document.write( "so, probably, you will not be happy. Therefore, let's try to use the Elimination method.\r\n" );
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document.write( "For it, multiply equation (1) by 3 (both sides), and multiply equation (2) by 2. You will get\r\n" );
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document.write( "    30x + 6y = 3*26.50    (3)\r\n" );
document.write( "    16x + 6y = 2*23.58    (4)\r\n" );
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document.write( "Now subtract equation (4) from equation (3).  The terms \" 6y \" will cancel each other (it is how the Elimination method works)\r\n" );
document.write( "and you will get\r\n" );
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document.write( "     30x - 16x = 3*26.50 - 2*23.58,   or\r\n" );
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document.write( "     14x = 32.34  =============>  x =  = 2.31.\r\n" );
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document.write( "Thus you found the price of one gallon of gas.\r\n" );
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document.write( "Now, in order for to find y, substitute the value x= 2.31  into either of the two equations (1) or (2).\r\n" );
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document.write( "I leave it to you to complete the solution on your own.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point I complete my instructions to you.\r
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\n" ); document.write( "\n" ); document.write( "Now you have a HAPPY OPPORTUNITY to make your horizon wider, regarding systems of equations and associated word problems.\r
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\n" ); document.write( "\n" ); document.write( "Look into my lessons in this site\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of the linear system of two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solving word problems using linear systems of two equations in two unknowns \r
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\n" ); document.write( "\n" ); document.write( "    - Oranges and grapefruits \r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on tickets \r
\n" ); document.write( "\n" ); document.write( "    - Three methods for solving standard (typical) problems on tickets\r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on shares \r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on investment\r
\n" ); document.write( "\n" ); document.write( "    - Two mechanics work on a car \r
\n" ); document.write( "\n" ); document.write( "    - The Robinson family and the Sanders family each used their sprinklers last summer\r
\n" ); document.write( "\n" ); document.write( "    - Roses and vilolets \r
\n" ); document.write( "\n" ); document.write( "    - Counting calories and grams of fat in combined food\r
\n" ); document.write( "\n" ); document.write( "    - A theater group made appearances in two cities\r
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\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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