Question

a. $x + 2y = 6$ and $x - y = 10$; b. $x + y = 6$ and $x - 2y = 10$; c. $x + 2y = 10$ and $x - y = 6$; d. $x + y = 6$ and $x - y = -10$

Explanation:

Step1: Analyze the blue line (first equation)

The blue line intersects the y - axis at (0, 6) and has a slope. Let's find its equation. Using the slope - intercept form \(y=mx + b\), where \(b = 6\) (y - intercept). Take two points, say (0, 6) and (4, 2). The slope \(m=\frac{2 - 6}{4-0}=\frac{- 4}{4}=-1\). So the equation is \(y=-x + 6\), which can be rewritten as \(x + y=6\).

Step2: Analyze the red line (second equation)

Let's find the intersection point of the two lines. From the graph, the intersection point seems to be at \(x=- 2,y = 8\) (by looking at the grid). Let's check the equations in option D: \(x + y=6\) (we already know this is the blue line's equation) and \(x-y=- 10\). Substitute \(x=-2,y = 8\) into \(x - y\): \(-2-8=-10\), which satisfies the equation. Let's check other options:

• Option A: For \(x + 2y=6\), when \(x = 0,y = 3\), but the blue line has y - intercept 6, so A is wrong.
• Option B: For \(x-2y = 10\), when \(x = 0,y=-5\), not matching the red line, so B is wrong.
• Option C: For \(x + 2y=10\), when \(x = 0,y = 5\), not matching the blue line, so C is wrong.

Answer:

D. \(x + y = 6\) and \(x - y=-10\)