How many solutions does the following system of equations have?
y = -3x + 8
y = -3x + 9
2006-12-28 15:43:05 · 9 answers · asked by shawnta b 1 in Science & Mathematics ➔ Mathematics
non
2006-12-28 15:47:32 · answer #1 · answered by M. Abuhelwa 5 · 0⤊ 0⤋
The system has no solutions.
If we plugged in y = -3x + 8 into the second equation, we would get
-3x + 8 = -3x + 9
Add 3x to both sides, and we'd get
8 = 9
Whenever the variable disappears in an equation, you look at the resulting answer and ask yourself, "is this true or false?" If the answer is false, there is no solution. If the answer is true, there is a solution.
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Now to go off on a tangent, take this example:
2x + 2y = 6
x + y = 3
Let's solve this by substitution. Solving for y in the second equation, y = 3 - x. Therefore, plugging this into the first equation,
2x + 2(3 - x) = 6
2x + 6 - 2x = 6
2x - 2x = 0
0 = 0
Our variable disappeared again; is the remaining statement true or false? It's true this time; that means there are infinitely many solutions (in fact, the solution is all real numbers).
2006-12-28 15:49:11 · answer #2 · answered by Puggy 7 · 0⤊ 0⤋
-5x + y = -5 -4x + 2y = 2 Use the technique of removing. Multiply all words interior the 1st equation with the aid of -2 to reason the y-words to cancel (do away with): 10x - 2y = 10 -4x + 2y = 2 upload words vertically: 6x = 12 x = 12/6 = 2 replace x = 2 into the two equation and clean up for y: -5(2) + y = -5 -10 + y = -5 y = -5 + 10 = 5 consequently, the answer is x = 2, y = 5, or (2,5).
2016-11-24 22:04:59 · answer #3 · answered by ? 4 · 0⤊ 0⤋
0 -- none. y = -3x + 8 = -3x + 9. It's an invalid statement (can't be equal to both). Therefore, there are no x and y combos that would solve the equation.
2006-12-28 15:46:19 · answer #4 · answered by Wendy C 2 · 0⤊ 0⤋
Zero.
8-3x = y = 9-3x ?
You can see that's impossible by adding 3x to both sides
8 = 9
2006-12-28 15:46:11 · answer #5 · answered by eldad9 6 · 0⤊ 0⤋
0
y=-3x + 8 and y=-3x+9 are parallel therefor they have no solution
2006-12-28 15:48:42 · answer #6 · answered by collieknutt 3 · 0⤊ 0⤋
none in standard math. that's like saying (assuming x = 1):
3 + 9 == 3 + 8
....
not possible.
You want to get into quantum mathematics ... well, it's too late for that tonight.
2006-12-28 15:48:49 · answer #7 · answered by worm22 2 · 0⤊ 0⤋
None. There's no value of (x,y) that equals both equations at the same time.
2006-12-28 15:46:38 · answer #8 · answered by j_orduna 2 · 0⤊ 0⤋
Infinite.Because x can be any number.
2006-12-29 01:34:20 · answer #9 · answered by Nitin T F1 fan 5 · 0⤊ 1⤋