Mathematics, 04.07.2019 07:10, lazavionadams81

Find the solution to the system of equations. select all that apply. y=x^2-2x-3. y=x-3

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answered: hollandhogenson

The solution to the system of equations are (0 , -3) ⇒ answer B and

(3 , 0) ⇒ answer D

Step-by-step explanation:

* Lets explain the problem

- The quadratic equation represented by parabola

- The linear equation represented by line

- If the two equation solved together, then we have 3 types of solutions

# They intersected in two different points (2 solution)

# They intersected in one point (1 solution)

# They did not intersect in any points (No solution)

* Now lets solve the problem

∵ The quadratic equation is y = x² - 2x - 3

- It represented by parabola (red graph)

∵ The linear equation is y = x - 3

- It represented by line (blue graph)

- The two graphs intersect each other at points (3 , 0) and (0 , -3)

∵ The solution of the system of the equation is the intersection points

between the two graphs

∵ The two graphs intersect each other at points (3 , 0) and (0 , -3)

∴ The solution to the system of equations are (3 , 0) and (0 , -3)

* The solutions are B and D

answered: Guest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

answered: Guest

8.4 10.4 8.9 10.9 have a good day

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Find the solution to the system of equations. select all that apply. y=x^2-2x-3. y=x-3
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