How many solutions does the system of equation have?
x-4y =12 and 5x-20y =60
To determine the number of solutions a system of equations has, we can solve the equations and check if they intersect at a single point, coincide (i.e., represent the same line), or do not intersect (parallel lines).
Let's solve the system of equations using the method of elimination:
Given equations:
1) x - 4y = 12
2) 5x - 20y = 60
We can simplify equation 2 by dividing both sides by 5:
2a) x - 4y = 12
Now, we have two identical equations: equation 1 and equation 2a. This means the system of equations represents the same line. When two equations coincide, the system has infinite solutions.
Therefore, the system of equations has infinite solutions.
same slope, same y intercept so lines on top of each other, infinite number of points
for heavens sake put your lines in the form y = m x + b and see if they have different m, slope
then if so, see if b is the same for both.