To solve a system of inequalities, it is necessary to find the ordered pairs that satisfies at least one of the inequalities in the system.

true or false?

true

Step-by-step explanation:

substitution method

A method used to solve systems of equations by solving an equation for one variable and substituting the resulting expression into the other equation(s).

y = 2x

y = x + 5

Step 1  

y = 2x

y = x + 5

Step 2

plug 2x into y = x + 5 for y

2x = x + 5

Step 3

solve for x

2x − x = x − x + 5

x = 5

Step 4

plug x = 5 into y = 2x

y = 2(5)

y = 10

Step 5

solution

(5, 10)

USE WHEN...

• A variable in either equation has a coefficient of 1 or −1.

• Both equations are solved for the same variable.

• Either equation is solved for a variable.

EXAMPLE

x + 2y = 7

x = 10 − 5y

or

x = 2y + 10

x = 3y + 5

elimination method

A method used to solve systems of equations in which one variable is eliminated by adding or subtracting two equations of the system.

x − 2y = −19

5x + 2y = 1

Step 1

x − 2y =−19

+5x + 2y = 1

∴ 6x + 0 =>−18

Step 2

6x = −18

6x ÷ 6 = −18 ÷ 6

x = −3

Step 3

plug x = -3 into x − 2y = −19

now, solve −3 − 2y = −19 for y

−3+ 3 − 2y = −19 + 3

−2y = −16

y = 8

Step 4

solution

(−3,8)

USE WHEN...

• Both equations have the same variable with the same or opposite coefficients.

• A variable term in one equation is a multiple of the corresponding variable term in the other equation.

EXAMPLE

3x + 2y = 8

5x + 2y = 12

or

6x + 5y = 10

3x + 2y = 15

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true