How many solutions as a system of equations have? 2X= -10y + 6 & x+5y=3
they are the same line, so ...
To find the number of solutions for a system of equations, we need to solve the system and see how many solutions it has.
Let's start by trying to solve the system of equations:
1) 2X = -10y + 6
2) X + 5y = 3
We can solve this system using the method of substitution or elimination. Let's use the method of substitution:
From equation 2), we can express X in terms of y:
X = 3 - 5y
Now, substitute this value of X into equation 1):
2(3 - 5y) = -10y + 6
Simplify the equation:
6 - 10y = -10y + 6
The variables -10y on both sides of the equation will cancel out, leaving us with:
6 = 6
Since the equation is true regardless of the value of y, this means that the system of equations is dependent. In other words, the two equations are essentially the same line and represent infinitely many solutions.
Therefore, the system of equations has infinitely many solutions.