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Download 1) Slope = (-2 +4) / (-5 + 5) = 2/0, the slope is undefined. 2)
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1) Slope = (-2 +4) / (-5 + 5) = 2/0, the slope is undefined. 2) -2x + 2y = 4, rearranging in intercept equation form, x/-2 + y/2 = 1 so x-intercept is -2 and y-intercept is 2 3) 2x - y = 6, rearranging in intercept-equation form, x/3 + y/-6 =1 So x-intercept is 3 and y-intercept is -6 4) 56 + 7y = 0, rearranging, y/-8 = 1 So only y-intercept exists and equal to -8 6) -3x + y = 14, rearranging in slope-intercept equation form, y = 3x + 14 So slope is 3 and y-intercept is 14 7) 2x+y = 5, rearranaging in intercept form, x/2.5 + y/5 = 1 So x-intercept is 2.5 and y-intercept is 5 8) Equation is y-9 = -8*(x-6) which solves to y +8x = 57 9) y = x+3 has slope 1. So this line’s slope would be -1. It passes through (2, -4), so equation is y +4 = -1 (x-2) which in slope-intercept form is y = -x -2 10) Plot two points (0, 2) and (2, 6) and draw a straight line passing through them. 11) 1990 means x=0, So one point is (0, 17). 1995 means x=5, so second point is (5, 23). Straight line passing through these two points is (y-17) = (23-17)x/5 Or y = 17 + 1.2x 12) y + 3 = (8+3)(x+5)/(-8+5) simplifying to slope intercept, y = -11/3 x - 64/3 14) x -5y = 4, x = 10+5y, substituting x from second eqn into first, (10+5y) – 5y = 4, or 10=4 which is wrong so system has no solution. 1) a+5b =2, 2a = -10b +4, substituting a from first eqn. into second, 2*(2-5b) = -10b + 4 4 – 10b = -10b + 4 Or 0 = 0. So it is true for all value of b. So, system has infinite number of solution. 2) -5r + 4s = 8 15r – 12 s = 24, Multiply first by 3 and adding to second, (-15r+12s)+(15r-12s) = 24+24 Or 0 = 48, which can’t be. So, system has no solution. 3) First number = x, second number = y. So, x-y = 88 y = 20x/100 = x/5 or x=5y Substituting x into first eqn. , 5y-y = 88 Or 4y = 88 Or y = 22 Putting this in first eqn. x = 88+22 = 110 So, first number is 110 and second number is 22. 4) Ron sold x tickets, Kathy sold y tickets. So, x+y = 364 And 2x + 4.5y = 1175.5 Multiplying first by 4.5 and subtracting 2nd by that gives, 4.5x + 4.5y –(2x+4.5y) = 1638-1175.5 Or 2.5x = 462.5 Or x = 185 So Ron sold 185 tickets. 5) Let he mix ‘x’ bags with 7% cement. Let the final number of bags of mix be y. So, x+ 10 = y x*7/100 + 10*15.5/100 = y*12/100 Substituing y=x+10 in 2nd equation and solving, 7x + 155 = 12x + 120 Or 5x = 35 Or x= 7 So he should mix 7 bags with 7% cement. 6) 3x+7y = 31 x-intercept 31/3 and y-intercept 31/7 5x-2y = -3 x-intercept -3/5 and y-intercept 3/2 To draw lines, plot x and y intercepts and make a straight line passing through them. Solve: Multiply first by 2 and second by 7 and add together, 6x+14y + 35x – 14y = 62 – 21 Or 41x = 41 Or x= 1 Putting in first equation, 3+7y = 31 Or y = 4 So intersection point is (1, 4) 7) x – 5y = -4 x-intercept is -4 and y-intercept is 4/5 x + 8y = -4 x-intercept is -4 and y-intercept is -1/2 Draw lines yourself as in last question. Solve: Subtract 2nd equation from 1st, x-5y – (x+8y) = -4 –(-4) or -13y = 0 or y = 0 putting in first eqn. x-0 = -4 or x = -4 So intersection point is (-4, 0) 8. 2x + y = 6, rearrange in xy intercept-form, x/3 + y/6 = 1. So x-intercept is 3 and yintercept is 6 9) 3(a-b) = 15 4a = b+1 Substituting b=4a-1 into first eqn., 3(a – (4a-1)) = 15 Or -3a + 1 = 5 Or a = -4/3 Putting in second eqn, b = -16/3 -1 = -19/3