3x-6y=6
6x-12y=15
and the other set is
2x-5y=-33
5x+2y=19
is there one solutions set, many or none?
3x-6y=6
6x-12y=15
This equation has no solution.....to see why....multiply the first equation by 2 on both sides...this gives 6x - 12y = 12
But the second equation says that the same quantity on the left hand side = 15. And one thing cannot equal two different things at the same time !!!
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2x-5y=-33
5x+2y=19
Let's multiply the top equation by 2 and the bottom equation by 5....this will eliminate y.......so we have
4x - 10y = -66
25x + 10y = 95 add the equations
29x = 29 divide both sides by 29
x = 1 and using the first equation to find y, we have
2(1) - 5y = - 33
2 - 5y = -33
-5y = -35 divide both sides by -5
y= 7
So...our solution is (1, 7)
3x-6y=6
6x-12y=15
This equation has no solution.....to see why....multiply the first equation by 2 on both sides...this gives 6x - 12y = 12
But the second equation says that the same quantity on the left hand side = 15. And one thing cannot equal two different things at the same time !!!
-----------------------------------------------------------------------------------------------------------------
2x-5y=-33
5x+2y=19
Let's multiply the top equation by 2 and the bottom equation by 5....this will eliminate y.......so we have
4x - 10y = -66
25x + 10y = 95 add the equations
29x = 29 divide both sides by 29
x = 1 and using the first equation to find y, we have
2(1) - 5y = - 33
2 - 5y = -33
-5y = -35 divide both sides by -5
y= 7
So...our solution is (1, 7)