1. We choose to substitute for y, because we have an equation that can easily be solved for y.
-2x + y = 13
y = 13 + 2x (add 2x to both sides)
2x + 5y = 29
2x + 5(13+2x) = 29
2x + 65 + 10x = 29
12x = 29 - 65
x = -36/12 = -3
y = 13 + 2(-3) = 13-6 = 7
The solution is (x, y) = (-3, 7)
2. 6x + y < -9, is (x, y) = (-4, 8) a solution?
6(-4) + (8) < -9
-24 + 8 < -9
-16 < -9 (true, so the ordered pair is a solution)
Ask her what she was thinking. She might have a way of looking at this that would surprise us. (It's not a crime. It's just different.)
(x, y) = (8, -4) is not a solution. 48 + (-4) < -9 is a false "sentence". The order you use to interpret the ordered pair matters. Conventionally, it is (x, y), but it can be specified to be something else.
-2x + y = 13
y = 13 + 2x (add 2x to both sides)
2x + 5y = 29
2x + 5(13+2x) = 29
2x + 65 + 10x = 29
12x = 29 - 65
x = -36/12 = -3
y = 13 + 2(-3) = 13-6 = 7
The solution is (x, y) = (-3, 7)
2. 6x + y < -9, is (x, y) = (-4, 8) a solution?
6(-4) + (8) < -9
-24 + 8 < -9
-16 < -9 (true, so the ordered pair is a solution)
Ask her what she was thinking. She might have a way of looking at this that would surprise us. (It's not a crime. It's just different.)
(x, y) = (8, -4) is not a solution. 48 + (-4) < -9 is a false "sentence". The order you use to interpret the ordered pair matters. Conventionally, it is (x, y), but it can be specified to be something else.