which graph shows the solution to the system of linear inequalities?\n$x - 4y \\leq 4$\n$y < x + 1$
which graph shows the solution to the system of linear inequalities?\n$x - 4y \\leq 4$\n$y < x + 1$
Answer
Explanation:
Step1: Analyze the boundary line of (x - 4y\leq4)
Rewrite (x - 4y = 4) as (y=\frac{1}{4}x - 1). Since the inequality is (\leq), the boundary line is solid.
Step2: Analyze the boundary line of (y\lt x + 1)
The equation (y=x + 1) is a straight - line. Since the inequality is (\lt), the boundary line is dashed.
Step3: Test a point for (x - 4y\leq4)
Take the origin ((0,0)): (0-4\times0=0\leq4), so the region containing ((0,0)) is part of the solution for (x - 4y\leq4).
Step4: Test a point for (y\lt x + 1)
Take the origin ((0,0)): (0\lt0 + 1) (True), so the region containing ((0,0)) is part of the solution for (y\lt x+1).
The first graph (the left - most one) has a solid line for (x - 4y = 4) (since (x-4y\leq4)), a dashed line for (y=x + 1) (since (y\lt x + 1)), and the overlapping region (the intersection of the regions defined by each inequality) is correctly shaded.
Answer:
The left - most graph.