document.write( "Question 829860: Find the constant s so that the lines (2x+4)x+5y= -7 and (s + 4)x+3y = s are parallel. \n" ); document.write( "
Algebra.Com's Answer #500229 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Find the constant s so that the lines (2x+4)x+5y= -7 and (s + 4)x+3y = s are parallel.\r\n" );
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document.write( "The first equation is a parabola, not a line. I suspect that it is a TYPO. I wonder if you \r\n" );
document.write( "mistakenly typed an x instead of an x inside the parentheses.\r\n" );
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document.write( "I will solve the problem with the first equation, (2s+4)x+5y= -7. If you have a different problem, you may email me and I'll help you sort it out.\r\n" );
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document.write( "SOLUTION:\r\n" );
document.write( "The key idea in this problem is that parallel lines have the same slope. We will put both \r\n" );
document.write( "equations in slope-intercept form (y=mx+b) and solve for s that makes the slopes the same \r\n" );
document.write( "in both equations.\r\n" );
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document.write( "(2s+4)x+5y= -7\r\n" );
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document.write( "Use distributive property to clear parentheses.\r\n" );
document.write( "2sx + 4x + 5y = -7\r\n" );
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document.write( "Combine like terms.\r\n" );
document.write( "(2s + 4)x + 5y = -7\r\n" );
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document.write( "Move the x-term to the right side by subtracting (2s+4)x.\r\n" );
document.write( "5y = -(2s + 4)x -7\r\n" );
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document.write( "Divide both sides by 5 to isolate y on the left.\r\n" );
document.write( "y = (-(2s + 4)/5)x - 7/5\r\n" );
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document.write( "Now translate the second equation to slope-intercept form.\r\n" );
document.write( "(s + 4)x+3y = s\r\n" );
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document.write( "Subtract (s+4)x from both sides.\r\n" );
document.write( "3y = -(s + 4)x + s\r\n" );
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document.write( "Divide both sides by 3 to isolate y on the left.\r\n" );
document.write( "y = (-(s + 4)/3)x + s/3\r\n" );
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document.write( "Both equations are in slope intercept form. Recall that the coefficient of the x-term is the \r\n" );
document.write( "slope of the equation. Since we want the slopes to be the same, set the expressions for the \r\n" );
document.write( "slope equal.\r\n" );
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document.write( "-(2s + 4)/5 = -(s + 4)/3\r\n" );
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document.write( "Let's clear the denominators first. The LCM of 3 and 5 is 15, so multiply both sides by 15.\r\n" );
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document.write( "-3(2s + 4) = -5(s + 4)\r\n" );
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document.write( "Use distributive property to clear the parentheses.\r\n" );
document.write( "-6s - 12 = -5s - 20\r\n" );
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document.write( "Solve for s. Add 12 to both sides.\r\n" );
document.write( "-6s - 12 + 12 = -5s - 20 + 12\r\n" );
document.write( "-6s = -5s - 8\r\n" );
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document.write( "Add 5s to both sides.\r\n" );
document.write( "-6s + 5s = -5s - 8 + 5s\r\n" );
document.write( "-s = -8\r\n" );
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document.write( "Multiply both sides by -1.\r\n" );
document.write( "s = 8\r\n" );
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document.write( "We want to check our work by substituting 8 for s in both original equations.\r\n" );
document.write( "(2s+4)x+5y= -7 and (s + 4)x+3y = s\r\n" );
document.write( "(2(8) + 4)x + 5y = -7 \r\n" );
document.write( "(16 + 4)x + 5y = -7\r\n" );
document.write( "20x + 5y = -7\r\n" );
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document.write( "Subtract 20x from both sides; divide each term by 5.\r\n" );
document.write( "5y = -20x - 7\r\n" );
document.write( "y = -4x - 7\r\n" );
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document.write( "AND\r\n" );
document.write( "(s + 4)x + 3y = s\r\n" );
document.write( "((8) + 4)x + 3y = (8)\r\n" );
document.write( "12x + 3y = 8\r\n" );
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document.write( "Subtract 12x from both sides; divide each term by 3.\r\n" );
document.write( "3y = -12x + 8\r\n" );
document.write( "y = -4x + 8/3\r\n" );
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document.write( "We see that the coefficient of the x-term for both equations in slope-intercept form is -4. Therefore, the lines are parallel when s = 8.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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