What is the solution of the following system?
{-2x - y = 1
{-4x - 2y = -1
a.) infinitely many solutions
b.) no solutions
c.) (3,8)
d.) (-3, -8)
To find the solution of the system, we can use the method of elimination.
First, let's multiply the first equation by -2 so that the coefficients of x in both equations are the same:
-2(-2x - y) = -2(1)
4x + 2y = -2
Now our system of equations is:
4x + 2y = -2 (Equation 1)
-4x - 2y = -1 (Equation 2)
If we add Equation 1 and Equation 2 together, the x terms cancel out:
(4x + 2y) + (-4x - 2y) = -2 + (-1)
0 = -3
This means that the system of equations is inconsistent, and there are no solutions.
Therefore, the correct answer is b.) no solutions.
To find the solution of the given system of equations, we can use the method of elimination or substitution.
Let's use the elimination method to solve the system:
1. Multiply the first equation by 2 to make the coefficients of y in both equations the same.
-2x - y = 1 (Multiply by 2)
-4x - 2y = -2
2. Rewrite the second equation after multiplying it by 2 to match the coefficients of y.
-4x - 2y = -1
3. Subtract the first equation from the second equation to eliminate the y term.
(-4x - 2y) - (-4x - 2y) = (-1) - (-2)
-4x - 2y + 4x + 2y = -1 + 2
0 = 1
The equation 0 = 1 is false, which means that the system of equations is inconsistent and has no solution.
Therefore, the answer is b.) no solutions.
double the first and you have
-4x-2y = 2
-4x-2y = -1
so, what do you think? Can -4x-2y be both?