2x-y=4 and 2x-y=3
We can solve this system by substitution:
if 2x - y = 4, we can manipulate this to arrive at:
=> 2x - 4 = y
Substitute in 2x - 4 to the second equation wherever we see a y:
If: 2x - y = 3
=> 2x -(2x - 4) = 3
=> 2x - 2x + 4 = 3
=> 4 = 3 ... This is obviously not true.
Thus, this system has no solution.
If you look at the lines in a different form:
y = 2x - 4
y = 2x - 3
You can see that we have two lines with the same slope: 2. They both begin at different y-intercepts: -4 and -3. Thus, they are parallel lines, and parallel lines do not intersect (meaning there is no solution to the system) unless they have the same y-intercept.
Hope that helps =)
To solve the system of equations:
1. Start by rewriting the equations in the standard form: Ax + By = C.
Equation 1: 2x - y = 4
Equation 2: 2x - y = 3
2. Set the two equations equal to each other, as the left side of both equations is the same.
2x - y = 4 = 2x - y = 3
3. From the equation, we can see that the expressions on both sides are equal, which means the two equations represent the same line. In this case, there are infinitely many solutions to the system of equations, as any point on the line will satisfy both equations simultaneously.
Therefore, the system of equations is consistent and dependent, and there are infinitely many solutions.
To find the values of x and y that satisfy the given system of equations, we can use the method of substitution or elimination. Let's solve it using the method of elimination:
1. Start by writing down both equations:
2x - y = 4 ...(Equation 1)
2x - y = 3 ...(Equation 2)
2. Notice that both equations have the same coefficients for x and y terms. We can subtract one equation from the other to eliminate one variable. Subtract Equation 2 from Equation 1 as follows:
(2x - y) - (2x - y) = 4 - 3
The x and y terms cancel out, and we are left with:
0 = 1
3. The resulting equation, 0 = 1, is not true. This means that there are no values of x and y that satisfy both equations simultaneously.
Hence, the system of equations is inconsistent, and there is no solution.