SOLUTION: Which pair of equations does NOT have a common solution? a) x+y = -1; 4x-3y=24 b)4x+6y=12; 6x+9y=12 c) 2x-3y=-4; 2x+y=4 d) 5x-4y=9; x-2y=-3 Please Explain solution Thank

Algebra ->  Real-numbers -> SOLUTION: Which pair of equations does NOT have a common solution? a) x+y = -1; 4x-3y=24 b)4x+6y=12; 6x+9y=12 c) 2x-3y=-4; 2x+y=4 d) 5x-4y=9; x-2y=-3 Please Explain solution Thank       Log On


   

Question 463148: Which pair of equations does NOT have a common solution?
a) x+y = -1; 4x-3y=24
b)4x+6y=12; 6x+9y=12
c) 2x-3y=-4; 2x+y=4
d) 5x-4y=9; x-2y=-3
Please Explain solution
Thank you!
Found 2 solutions by richard1234, MathLover1:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Already posted. Even with the changes in C, B does not have a common solution.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Which pair of equations does NOT have a common solution?
a)
x%2By+=+-1; 4x-3y=24
b)4x%2B6y=12; 6x%2B9y=12
c) 2x-3y=-4; 2x%2By=4
d) 5x-4y=9; x-2y=-3
easiest way is to write all of them in slope-intercept form and see if any of them are parallel lines; parallel lines do NOT have a common solution

a)
y+=-x-1...slope is -1
4x-24=3y
%284%2F3%29x-8=y..slope is %284%2F3%29

b)
4x%2B6y=12...6y=-4x%2B12...y=-%284%2F6%29x%2B2.y=-%282%2F3%29x%2B2...slope is -%282%2F3%29

6x%2B9y=12.....9y=-6x%2B12...y=-%286%2F9%29x%2B12%2F9...y=-%282%2F3%29x%2B4%2F3...slope is -%282%2F3%29

c)
2x-3y=-4 .....2x%2B4=3y .....%282%2F3%29x%2B4%2F3=y ...slope is %282%2F3%29
2x%2By=4...y=-2x%2B4...slope is -2


d)
5x-4y=9....5x-9=4y...%285%2F4%29x-9%2F4=y..slope is %285%2F4%29
x-2y=-3.....x%2B3=2y.....%281%2F2%29x%2B3%2F2=y.slope is %281%2F2%29
as you can see, only
b)
4x%2B6y=12 and 6x%2B9y=12 have same slope..
let's see if these lines are parallel:


so, your answer is b