Question

the equations \\(y = 2x - 5\\) and \\(y = \sqrt{3x - 1}\\) are graphed on the coordinate grid.

how many real solutions does the equation \\(\sqrt{3x - 1} = 2x - 5\\) have?

( ) 0
( ) 1
( ) 2
( ) cannot be determined from the graph

Explanation:

Identify the relationship between the equation and the graph

The real solutions to the equation \(\sqrt{3x - 1} = 2x - 5\) correspond to the \(x\)-coordinates of the intersection points of the two graphed curves:

$$ y = \sqrt{3x - 1} \quad \text{and} \quad y = 2x - 5 $$

Count the number of intersection points from the graph

By observing the coordinate grid:

• The line \(y = 2x - 5\) and the radical curve \(y = \sqrt{3x - 1}\) intersect at exactly one point.
• This intersection point is located at \((4, 3)\).
• There are no other points where the two graphs cross or touch.

Determine the number of real solutions

Since there is exactly one intersection point on the graph, the equation has exactly 1 real solution.

Answer:

• 0
• 1 (Correct answer)
• 2
• cannot be determined from the graph