How many solution are there in the following system of equations?
x=-6y+4
2x+12y=8
Please help me and explain it to me! I would really appreciate if you guys answered it!
rearrange things to a single format:
x+6y=4
2x+12y=8
Now you can see that they are really the same line.
So are there infinite solutions?
correct.
To find the number of solutions in the given system of equations, let's solve the system using the method of substitution:
Step 1: Start with the first equation x = -6y + 4.
Step 2: Substitute x in the second equation with -6y + 4:
2(-6y + 4) + 12y = 8.
Step 3: Simplify and solve this equation:
-12y + 8 + 12y = 8,
8 = 8.
Step 4: The equation in step 3 simplifies to 8 = 8. This means that the equation is always true, regardless of the value of y. In other words, this equation represents an identity.
Step 5: Since we have an identity, it implies that the given system of equations has infinitely many solutions.
Explanation: The given system of equations has infinitely many solutions because when we substitute the value of x in the second equation, we end up with an identity (an equation that is always true). Therefore, any value of y can be chosen, and there will always be a corresponding value of x that satisfies both equations.