Since the system has infinite solutions, the equations must represent the same line or have overlapping lines. Let's solve the equations and see if they represent the same line:
Equation 1: 4x + 2y = 6
Equation 2: 2x + y = 3
To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution:
From Equation 2, we can isolate y as follows:
y = 3 - 2x
Now, substitute this value of y into Equation 1:
4x + 2(3 - 2x) = 6
4x + 6 - 4x = 6
6 = 6
As we can see, both equations are consistent and they simplify to the same equation, 6 = 6. This means the two equations represent the same line. Therefore, the system has infinite solutions.
Consider the two equations you circled, which form a system with infinite solutions.
Solve the equations.
1 answer