# SOLUTION: Find the constant s so that the lines (2x+4)x+5y= -7 and (s + 4)x+3y = s are parallel.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Find the constant s so that the lines (2x+4)x+5y= -7 and (s + 4)x+3y = s are parallel.      Log On

 Question 829860: Find the constant s so that the lines (2x+4)x+5y= -7 and (s + 4)x+3y = s are parallel. Answer by math-vortex(647)   (Show Source): You can put this solution on YOUR website! ```Hi, there-- THE PROBLEM: Find the constant s so that the lines (2x+4)x+5y= -7 and (s + 4)x+3y = s are parallel. The first equation is a parabola, not a line. I suspect that it is a TYPO. I wonder if you mistakenly typed an x instead of an x inside the parentheses. 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. SOLUTION: The key idea in this problem is that parallel lines have the same slope. We will put both equations in slope-intercept form (y=mx+b) and solve for s that makes the slopes the same in both equations. (2s+4)x+5y= -7 Use distributive property to clear parentheses. 2sx + 4x + 5y = -7 Combine like terms. (2s + 4)x + 5y = -7 Move the x-term to the right side by subtracting (2s+4)x. 5y = -(2s + 4)x -7 Divide both sides by 5 to isolate y on the left. y = (-(2s + 4)/5)x - 7/5 Now translate the second equation to slope-intercept form. (s + 4)x+3y = s Subtract (s+4)x from both sides. 3y = -(s + 4)x + s Divide both sides by 3 to isolate y on the left. y = (-(s + 4)/3)x + s/3 Both equations are in slope intercept form. Recall that the coefficient of the x-term is the slope of the equation. Since we want the slopes to be the same, set the expressions for the slope equal. -(2s + 4)/5 = -(s + 4)/3 Let's clear the denominators first. The LCM of 3 and 5 is 15, so multiply both sides by 15. -3(2s + 4) = -5(s + 4) Use distributive property to clear the parentheses. -6s - 12 = -5s - 20 Solve for s. Add 12 to both sides. -6s - 12 + 12 = -5s - 20 + 12 -6s = -5s - 8 Add 5s to both sides. -6s + 5s = -5s - 8 + 5s -s = -8 Multiply both sides by -1. s = 8 We want to check our work by substituting 8 for s in both original equations. (2s+4)x+5y= -7 and (s + 4)x+3y = s (2(8) + 4)x + 5y = -7 (16 + 4)x + 5y = -7 20x + 5y = -7 Subtract 20x from both sides; divide each term by 5. 5y = -20x - 7 y = -4x - 7 AND (s + 4)x + 3y = s ((8) + 4)x + 3y = (8) 12x + 3y = 8 Subtract 12x from both sides; divide each term by 3. 3y = -12x + 8 y = -4x + 8/3 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. Hope this helps! Feel free to email if you have any questions about the solution. Good luck with your math, Mrs. F math.in.the.vortex@gmail.com ```