Question

In graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded ad labeled B, and the area where f(x) and g(x) have shading in common is labeled AB

the graph represents which system of inequalities?

y≤-2x+3
y≤x+3

y≥-2x+3
y≥x+3

y≤-3x+2
y≤-x+2

y>-2x+3
y>x+3​​​

Answer 1

The graph represents the system of inequalities y ≤ -3x + 2 and y ≤ -x + 2 ⇒ C

Explanation:

From the given figure

∵ The direction of each line is to left

∴ The slopes of the lines are negative

∵ The slope of the line is the coefficient of x

∴ The coefficient of x in each inequality is negative ⇒ (1)

∵ The two lines intersect the y-axis at the point (0, 2)

∴ The y-intercept of the two lines is (0, 2)

∵ The y-intercept is the numerical term in the equation

∴ The numerical term in each inequality is 2 ⇒ (2)

∵ The two lines are solids

∵ The shaded area of each one is under the line

∴ The sign of inequality in both equations is ≤ ⇒ (3)

→ Look at the answer and find which one has the 3 conditions above

∵ y ≤ -3x + 2 and y ≤ -x + 2

∴ m = -3 and m = -1 ⇒ negative coefficients of x

∴ b = 2 ⇒ numerical term

∵ The sign of inequality is ≤

∴ The graph represents the system of inequalities y ≤ -3x + 2 and y ≤ -x + 2