how many solutions does the system of equations have y=4x+3 and 2y - 8x=3
To find the number of solutions the system of equations has, we can solve the equations simultaneously:
We are given the equations:
1) y = 4x + 3
2) 2y - 8x = 3
First, let's substitute the value of y from equation 1) into equation 2):
2(4x + 3) - 8x = 3
8x + 6 - 8x = 3
6 = 3
This simplifies to 6 = 3, which is not a true statement. It means that the equations are inconsistent, and therefore the system has no solution. Thus, the system of equations has 0 solutions.
To determine the number of solutions for the system of equations, we can solve the equations simultaneously and analyze the result.
1. Rearrange the first equation to isolate y:
y = 4x + 3
2. Substitute the value of y from the first equation into the second equation:
2(4x + 3) - 8x = 3
3. Simplify and solve for x:
8x + 6 - 8x = 3
6 = 3
4. Thus, we have obtained a contradiction: 6 does not equal 3.
Since the equation simplifies to a contradiction, there are no solutions for this system of equations. It means that the two lines represented by these equations do not intersect and are parallel to each other on the coordinate plane.