For each system of equations, drag the true statement about its solution set to the box under the system.
One Solution:
The graphs of these lines would intersect at one point.
Infinitely Many Solutions:
Both the right and left sides of the equations are equivalent expressions.
Zero Solutions:
y is equal to two different expressions.
Zero Solutions:
2x + 4 = x + 4 has no solutions.
Infinitely Many Solutions:
2x + 4 is a multiple of x + 4.
To match the true statements to the correct systems of equations, let’s break down each option:
1. One Solution:
The graphs of these lines would intersect at one point.
– This is true for a system with two lines that are not parallel; they intersect at a single point.
2. Infinitely Many Solutions:
Both the right and left sides of the equations are equivalent expressions.
– This is true for a system where both equations represent the same line, meaning every point on the line is a solution.
3. Zero Solutions:
y is equal to two different expressions.
– This is correct when the left-hand sides of two equations lead to a contradiction (like y = 2 and y = 3).
4. Zero Solutions:
2x + 4 = x + 4 has no solutions.
– This statement is true because when you simplify it (subtracting x and 4 from both sides), you get x = 0 = x, which leads to a contradiction.
5. Infinitely Many Solutions:
2x + 4 is a multiple of x + 4.
– This is true because you could express both equations in such a way that they represent the same line.
So, the assignments would be:
– One Solution: The graphs of these lines would intersect at one point.
– Infinitely Many Solutions: Both the right and