describe the solution to this system of equations:

Question

8x-2y=-4
4x-y=-2

A. solve this system by elimination since it is already in standard form and lined up nicely.
B. solve this system by subsitution since one of the variables is defined by the other without having to do any math.

Answer 1

The solution to this system of equations can be found by using the method of substitution.

First, we can solve one of the equations for one variable in terms of the other. Let's solve the second equation for y:

4x - y = -2
y = 4x + 2

Now, we substitute this expression for y into the first equation:

8x - 2(4x + 2) = -4
8x - 8x - 4 = -4
-4 = -4

Both sides of the equation are equal, which means that the system of equations is consistent and the two equations represent the same line. Therefore, there are infinitely many solutions to this system, and the solution is all values of x and y that satisfy the equations.

In conclusion, the solution to the system of equations is B. solve this system by substitution since one of the variables is defined by the other without having to do any math.