How do I find the solution for -2x-4y=1 12y=-6x-3?
you can see that -2x = 1+4y
So, -6x = 3+12y
Now substitute that into the 2nd equation and solve for y.
To find the solution for the system of equations:
-2x - 4y = 1 ----(1)
12y = -6x - 3 ----(2)
There are a few different methods you can use to find the solution, such as substitution, elimination, or using matrices. Here, I will explain how to solve it using the substitution method:
Step 1: Solve one equation for one variable
Let's solve equation (2) for y:
12y = -6x - 3
Divide both sides of the equation by 12:
y = (-6x - 3) / 12
Simplify the right-hand side:
y = (-1/2)x - 1/4
Step 2: Substitute the expression for y into the other equation
Now, substitute the expression for y from equation (2) into equation (1):
-2x - 4((-1/2)x - 1/4) = 1
Distribute the -4:
-2x + 2x + 1 = 1
Combine like terms:
1 = 1
Since the equation is true, this means that the system of equations is dependent, and there are infinitely many solutions. In other words, any value of x can be chosen, and the corresponding value of y can be calculated using the equation y = (-1/2)x - 1/4.
So, the solution to the system of equations is given by the equation y = (-1/2)x - 1/4, where x can be any real number.