How many solutions does the system of equations have?
3x+15y=35 and y=-1/5x+7/3
We can first solve the second equation for x in terms of y:
y=-1/5x+7/3
1/5x=7/3-y
x=35-5y
Now we can substitute this expression for x into the first equation:
3(35-5y)+15y=35
105-15y+15y=35
105=35
This is a contradiction and there are no solutions to the system of equations.
To determine the number of solutions for the system of equations, we can solve them and see if they intersect at a point, are parallel, or coincide.
Let's start by substituting the value of y from the second equation into the first equation:
3x + 15(-1/5x + 7/3) = 35
Simplifying the equation:
3x - 3x + 35 = 35
Since both variables cancel out, we are left with:
35 = 35
The resulting equation is always true, which means that these two equations are actually the same line and coincide. Therefore, the system of equations has infinitely many solutions.