solve by elimination method.
5x+6y=3
10x+12y=6
To solve this system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant to make the coefficients of one of the variables in the two equations the same.
Looking at the coefficients of "x" in both equations, the coefficients are already the same.
Step 2: Add or subtract the two equations to eliminate one variable.
Let's eliminate the "x" variable by multiplying the first equation by (-2). This will make the coefficients of "x" in both equations opposite:
-2 * (5x + 6y) = -2 * 3
-10x - 12y = -6
Now, we have two equations:
-10x - 12y = -6
10x + 12y = 6
When we add these two equations together, the "x" variable is eliminated:
-10x - 12y + 10x + 12y = -6 + 6
0 = 0
Step 3: Analyze the result.
The equation 0 = 0 means that it is always true, regardless of the values of "x" and "y". This indicates that the two original equations are actually representing the same line and have infinitely many solutions. In other words, this system of equations is dependent and has infinitely many solutions.
Therefore, there are infinitely many pairs of values (x, y) that satisfy these equations.
5x+6y=3 Multiply both sides with -2
-10x-12y= -6
-10x+12y= -6
+
10x+12y=12
(-10x+10x)+(-12y+12y)= -6+6
0+0=0
0=0
This is called an "inconsistent" system of equations, and it has no solution.