Final answer:
Neither System 1 nor System 2 has no solution as they both describe lines that either intersect or are identical. System 1's equations have different slopes and System 2's equations are identical, indicating the latter has infinitely many solutions.
Step-by-step explanation:
To determine which system of linear equations has no solution, let's analyze each system separately. A system of equations has no solution if the lines represented by the equations are parallel, which implies they have the same slope but different y-intercepts.
System 1: Consists of the equations x + 2y = 3 and x + y - 3 = 4. If we put these equations in the form y = mx + b, where m is the slope and b is the y-intercept, we get:
- x + 2y = 3 → 2y = -x + 3 → y = -0.5x + 1.5
- x + y = 7 → y = -x + 7
Both equations have different slopes (-0.5 and -1), so they are not parallel, and there must be a solution where they intersect.
System 2: Consists of the equations 5x + y = 13 and 20x = 52 - 4y. Converting the second equation into y = mx + b form, we have:
- 5x + y = 13 → y = -5x + 13
- 20x + 4y = 52 → 4y = 52 - 20x → y = -5x + 13
Notice that both equations are identical, meaning they represent the same line and have infinitely many solutions.
Therefore, the answer to which system of linear equations has no solution is (D) Neither System 1 nor System 2 has a solution.