Final answer:
To find the solution to the linear system using the x- and y-intercepts, we need to find the points where each equation intersects the x-axis and y-axis. The point that represents the solution to the linear system using the x- and y-intercepts is the point where both intercepts intersect. The correct answer is (0, -3/2).
Step-by-step explanation:
To find the solution to the linear system using the x- and y-intercepts, we need to find the points where each equation intersects the x-axis and y-axis. To find the x-intercept, set y = 0 and solve for x. For the first equation, x - 4y = 6, we have x - 4(0) = 6, which simplifies to x = 6. So the x-intercept for this equation is (6, 0).
Similarly, for the second equation, 1 - 2x + y = 2, we have 1 - 2x + 0 = 2, which simplifies to -2x = 1. x = 1/(-2), so the x-intercept for this equation is (-1/2, 0).
To find the y-intercept, set x = 0 and solve for y. For the first equation, x - 4y = 6, we have 0 - 4y = 6, which simplifies to -4y = 6. y = 6/(-4), so the y-intercept for this equation is (0, -3/2).
For the second equation, 1 - 2x + y = 2, we have 1 - 2(0) + y = 2, which simplifies to 1 + y = 2. y = 2 - 1, so the y-intercept for this equation is (0, 1).
The point that represents the solution to the linear system using the x- and y-intercepts is the point where both intercepts intersect. On comparing the intercepts of both equations, we can see that the point (0, -3/2) is common to both equations. Therefore, the correct answer is (0, -3/2).