A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.
Let's look at the four equations, with each solved as needed, into y = mx + b form.
A: 2x + y = 5
y = 5 - 2x
y = -2x + 5
Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.
B: y = 2x + 5
Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.
C: 2x - 4y = 10
-4y = 10 - 2x
-4y = -2x + 10
y = 2/4x -10/4
Here the slopes are different, so, like A this is not a good choice.
D: 2y - 4x = -10
2y = =10 + 4x
2y = 4x - 10
y = 2x - 5
Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.
Thus, D is the best choice.
If you would like to write each rate as a unit rate, you can do this using the following steps:
$2 ... 5 cans of a soup
$1 ... x cans of a soup = ?
2 * x = 5 * 1
2 * x = 5
x = 5 / 2
x = 2.5 cans of a soup per $1
$2 ... 5 cans of a soup
$x = ? ... 1 can of a soup
2 * 1 = 5 * x
2 = 5 * x
x = 2 / 5
x = $0.4 per 1 can of a soup
Let x represent the amount to be added. The total amount of tin will be
15%·20 + 10%·x = 12%·(20+x)
(15%-12%)·20 = (12%-10%)·x
3%·20/2% = x
30 = x
30 pounds of 10% tin must be added to get a 12% mixture.
The answer must be -52 because I added parenthesis around -3 × 6 so it won't confuse people. I multiplied -3 and 6 and got -18. Then I multiplied -18 and 3 and got -54. I add -54 and 2 and got -52. Since there's more of negative than positive, I subtracted and got -52. Hope this helps :)
