document.write( "Question 825786: On a graph paper, draw the two straight lines which represent the equations 2x – y = 3 and
\n" ); document.write( "3x + 2y = 1. Also, find their point of intersection of the two lines on the graph paper. \n" ); document.write( "

Algebra.Com's Answer #497722 by math-vortex(648) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "On a graph paper, draw the two straight lines which represent the equations 2x – y = 3 and\r\n" );
document.write( "3x + 2y = 1. Also, find their point of intersection of the two lines on the graph paper.\r\n" );
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document.write( "A SOLUTION:\r\n" );
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document.write( "I like to rewrite the equations in slope-intercept form because it makes them easy to graph.\r\n" );
document.write( "Start with the first equation:\r\n" );
document.write( "2x - y = 3\r\n" );
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document.write( "Subtract 2x from both sides.\r\n" );
document.write( "-y = -2x = 3\r\n" );
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document.write( "Multiply both sides by -1.\r\n" );
document.write( "y = 2x - 3\r\n" );
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document.write( "Now, the second equation:\r\n" );
document.write( "3x + 2y = 1\r\n" );
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document.write( "Subtract 3x from both sides.\r\n" );
document.write( "2y = -3x + 1\r\n" );
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document.write( "Divide both sides by 2.\r\n" );
document.write( "y = (-3/2)x + (1/2)\r\n" );
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document.write( "Here is a graph of the two lines:\r\n" );
document.write( "The first line (red) has a slope of 2, and a y-intercept at (0,-3).\r\n" );
document.write( "The second line (green) has a slope of -3/2 and a y-intercept of 1/2.\r\n" );
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document.write( "It appears that the lines intersect near (1,-1).\r\n" );
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document.write( "We can verify that with algebra:\r\n" );
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document.write( "Substitute 1 for x and -1 for y in both equations:\r\n" );
document.write( "2x – y = 3 -----> 2(1) - (-1) = 3 -----> 2 + 1 = 3 TRUE!\r\n" );
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document.write( "3x + 2y = 1 ---> 3(1) + 2(-1) = 1 ----> 3 - 2 = 1 TRUE!\r\n" );
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document.write( "Yes, (1,-1) is the intersection point of the two lines.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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