Download 1) Slope = (-2 +4) / (-5 + 5) = 2/0, the slope is undefined. 2)

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