How many solutions does the system of equations have?
3x+12y=20
y=-1/4x+5/3
They are the same line.
so infinite?
It was zero. If both equations are on the same line it is zero
To determine the number of solutions for the system of equations, we need to analyze the relationship between the two equations.
The first equation is in standard form: 3x + 12y = 20.
The second equation is in slope-intercept form: y = -1/4x + 5/3.
We can see that the second equation is already solved for y. Therefore, we can substitute this expression for y into the first equation to obtain:
3x + 12(-1/4x + 5/3) = 20.
Simplifying the equation gives us:
3x - 3x + 20 = 20,
0 = 0.
The equation simplifies to 0 = 0, which is a true statement. This indicates that the two equations represent the same line.
When two equations represent the same line, it means that they are equivalent and have infinitely many solutions. In other words, every point on one line is a solution to both equations.