ALGEBRA MATH solve by elimination method 5x+6y=3 10x+12y=6?

5x+6y=3.....(i)
10x+12y=6.....(ii)
using the elimination method
equation (i) * 2
10x+12y=6.....(iii)
equation (iii) - (i)
10x+12y=6
- 10x+12y=6 -
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0=0
no solution

k you should know the answer by now, but some people are saying no solutions, shouldn't it be infinite since they are on the same line.

These equations are one and the same.

Infinite number of solutions.

5x + 6y = 3
10x + 12y = 6

5x + 6y = 3
2(5x + 6y) = 2(3)
10x + 12y = 6

...10x + 12y = 6
‒) 10x + 12y = 6 (subtraction)
----------------------------
0
(infinite solutions)

the second equation is the first multiplied by two. It is the same line. The solution is all points on the line.

5c+6y=3 10x+12y=6 If you double the coefficients in the top equation, you will see that these are in fact the same line. Therefor, there is no single solution. Generally, one just puts "no unique solutions" for the answer, since the lines are the same. Another way to look at it is this, If you put both in slope-intercept form, you get y=-5/6x+1/2 for each, showing that the two equations represent the same line

[5x+6y=3]*2
=>10x+12y=6 which is equal to first equation and thus the lines are
coincident. they have infinitely many solutions. all the points on the line are solutions.

these are the rules:
for 2 lines in the form a1x+b1y=c1
& a2x+b2y=c2
the rules are:
1. a1/a2 not equal to b1/b2, unique [one] solution[intersecting lines]
2. a1/a2=b1/b2=c1/c2, infinitely many solutions[coincident lines]
3. a1/a2=b1/b2 not eq. to c1/c2, no solution[since they are parallel lines]

5x + 6y = 3 ----> eq'n A
10x + 12y = 6 -> eq'n B
A : 5x + 6y = 3
-B/2: -5x - 6y = -3 (then add both equations)
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0 = 0 -----> the two equations are equivalent, meaning apply the same values of x and same values of y in both equations and both will become true, they're equivalent after all

The ordered pair (0,0) means that in the cartesian plane, the point is located in the intersection of the lines x = 0 and y = 0 (which means it is in the origin, or where the x and y axes meet)

no solution.

multiply the first equation by neg 2
both variables drop out