-x+y=-2
4x-4y=8
WHAT ARE THE SOLUTIONS OF THE FOLLOWING SYSTEM?
To find the solutions of the given system of equations, we can use the method of elimination or substitution.
Let's solve the system of equations using the method of elimination:
Step 1: Multiply both sides of the first equation by 4 to make the coefficients of x in both equations the same:
-4x + 4y = -8
Step 2: Add the new equation obtained in Step 1 to the second equation:
-4x + 4y + 4x - 4y = -8 + 8
0 = 0
The equation 0 = 0 is always true regardless of the values of x and y. This means that the two given equations are actually representing the same line in the coordinate plane. Since they are identical, they have an infinite number of solutions.
In summary, the given system of equations has infinitely many solutions.
Add x and 2 to both sides of the first equation.
x = y + 2
4x -4y = 8
Substitute y+2 for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.