document.write( "Question 170730This question is from textbook Intermediate Algebra
\n" ); document.write( ": I'm 60 years old and I decided to go back to show and this math is a little hard please please help.\r
\n" ); document.write( "\n" ); document.write( " Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result. \r
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\n" ); document.write( "\n" ); document.write( "thank you in advance.
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Algebra.Com's Answer #126038 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Start with the given system of equations:\r
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\n" ); document.write( "\n" ); document.write( " $\"system%284x-6y=2%2C2x-3y=1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In order to graph these equations, we must solve for y first.\r
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\n" ); document.write( "\n" ); document.write( "Let's graph the first equation:\r
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\n" ); document.write( "\n" ); document.write( " $\"4x-6y=2\"$ Start with the first equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"-6y=2-4x\"$ Subtract $\"4x\"$ from both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282-4x%29%2F%28-6%29\"$ Divide both sides by $\"-6\"$ to isolate $\"y\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%2F3%29x-1%2F3\"$ Rearrange the terms and simplify.\r
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\n" ); document.write( "\n" ); document.write( "Now let's graph the equation:\r
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Graph of $\"y=%282%2F3%29x-1%2F3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's graph the second equation:\r
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\n" ); document.write( "\n" ); document.write( " $\"2x-3y=1\"$ Start with the second equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"-3y=1-2x\"$ Subtract $\"2x\"$ from both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281-2x%29%2F%28-3%29\"$ Divide both sides by $\"-3\"$ to isolate $\"y\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%2F3%29x-1%2F3\"$ Rearrange the terms and simplify.\r
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\n" ); document.write( "\n" ); document.write( "Now let's graph the equation:\r
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Graph of $\"y=%282%2F3%29x-1%2F3\"$ (red). Graph of $\"y=%282%2F3%29x-1%2F3\"$ (green)\r
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\n" ); document.write( "\n" ); document.write( "From the graph, we can see that one line is right on top of the other one, which means that they intersect an infinite number of times. \r
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\n" ); document.write( "\n" ); document.write( "So there are an infinite number of solutions. This means that the system of equations is consistent and dependent.\r
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