Which system of equations does this graph represent?

The system of equations is y = x - 4 and y = x² - 6

Step-by-step explanation:

The graph has a linear equation represented by a line and a quadratic equation represented by a parabola

The form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

The form of the quadratic equation is y = a(x - h)² + k, where (h, k) are the coordinates of its vertex point and a is the coefficient of x²

let us use the graph to find each equation

→ Equation the line

∵ The line passes through points (-1, -5) and (2, -2)

∵ m =

∴ m =

∴ m = 1

∵ The line intersected the y-axis at point (0, -4)

∵ b is the value of y at x = 0

∴ b = -4

→ Substitute the values of m and b in the form of the equation above

∴ y = (1)x + (-4)

∴ y = x - 4

→ Equation the parabola

∵ The vertex of the parabola is (0, -6)

∴ h = 0 and k = -6

→ Substitute them in the equation

∴ y = a(x - 0)² + -6

∴ y = ax² - 6

→ To find a choose any point on the parabola and substitute x and y

   by its coordinated

∵ The point (2, -2) lies on the parabola

∴ x = 2 and y = -2

∵ -2 = a(2)² - 6

∴ -2 = 4a - 6

→ Add 6 to both sides

∵ -2 + 6 = 4a - 6 + 6

∴ 4 = 4a

→ Divide both sides by 4

∴ 1 = a

∴ y = (1)x² - 6

∴ y = x² - 6

The system of equations is y = x - 4 and y = x² - 6

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!