-3x + y = 7
6x -2y = -14
--------------
-3x + y = 7
y = 7 + 3x
6x -2(7 + 3x) = -14
6x - 14 + -6x = -14
0 = 0
Or is that many solutions?
2007-12-19 11:34:51 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Should I go on to find y? Or is the answer just NO SOLUTION?
2007-12-19 11:35:33 · update #1
Can I solve it using the addition method?******
2007-12-19 11:36:32 · update #2
Those two equations are actually the same. Multiply the top one through by -2 and you will see
2007-12-19 11:39:41 · answer #1 · answered by Anonymous · 0⤊ 2⤋
You're actually left off with 0x = 0, which means there are an infinite number of solutions.
Using the addition (or subtraction) method, multiplying the first equation by -2
6x - 2y = -14
6x - 2y = -14
-------------------
0 = 0
These equations are identical to each other, so there are an infinite number of solutions.
2007-12-19 19:39:47 · answer #2 · answered by Jacob A 5 · 0⤊ 1⤋
The equations are coincident. That means they are identical and the same line. It also means that any solution to
y = 3x + 7 is valid.
Here is how they are coincident:
6x - 2y = -14
3x - y = -7
y = 3x + 7
2007-12-19 19:42:05 · answer #3 · answered by Lane 3 · 0⤊ 1⤋
The two equations are essentially identical. If you multiply the first by -2 on both sides, you get the second equation exactly. Therefore, any x and y satisfying the first will satisfy the second. X = 1 and Y = 10 for example, will work in both equations.
2007-12-19 19:51:38 · answer #4 · answered by Snickers 1 · 0⤊ 1⤋
actually, if you multiply the first equation with -2, you obtain the second equation.
So the both equations are equivalent.
The system has a solution, an infinity of solutions
make -3x = -7-y
x = (7+y)/3
so you have solutions all the pairs
((7+y)/3, y)
2007-12-19 19:41:08 · answer #5 · answered by Theta40 7 · 0⤊ 1⤋
The second equation can be put into the form
-3x-2y=7
by multiplying by -.5 so there is an infinite number of solutions because you have one equation in two unknowns.
2007-12-19 19:46:08 · answer #6 · answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6 · 0⤊ 1⤋
(1) -3x + y = 7
(2) 6x - 2y = -14
(2) is merely (1) multiplied by -2
You cannot solve a series of equations if the given equations are just multiples of each other as this is really the same equation (if you simplify (2) you get (1) in this case).
This system cannot be solved explicitly.
2007-12-19 19:39:04 · answer #7 · answered by disposable_hero_too 6 · 0⤊ 2⤋
0=0 is the correct answer.
if you use combination
the x and y cancel out
so 0=0
2007-12-19 19:38:20 · answer #8 · answered by Dylan K 2 · 0⤊ 2⤋
no solution
2007-12-19 22:21:34 · answer #9 · answered by BrushPicks 5 · 0⤊ 1⤋