`y < 2x + 3` Determine whether (0, 0) satisfies each inequality.

Textbook Question

Chapter 2, 2.6 - Problem 60 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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philiostratus's profile pic

philiostratus | High School Teacher | (Level 1) Adjunct Educator

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A solution will satisfy an inequality only when it makes it true.

This is tested by substituting in the values to be tested, in this case x=0 and y=0 into the inequality y<2x+3.

Substitution gives us (0)<2(0)+3.

Multiplying we get (0)<(0)+3.

Then adding, 0<3. 

Since this inequality is true the solution (0,0) satisfies the inequality.

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dbrock1 | High School Teacher | (Level 1) Adjunct Educator

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To determine whether any ordered pair is a solution to an equation or inequality, simply substitute the values into the equation or inequality and then determine if the statement is true.  If it is true, then the ordered pair is a solution. If it is false, then the ordered pair is not a solution.

in the ordered pair, (0,0) the first term is the x value and the second term is the y value. In this case both x and y have the value of 0. Substitute 0 in place of both x and y in the inequality and the statement becomes:

0 < 2(0) + 3

this simplifies to 0 < 0 + 3 which then simplifies to 0 < 3. Since zero is, in fact, less than 3, then the ordered pair, (0,0) definitely satisfies the inequality.

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sschall | Middle School Teacher | (Level 1) Adjunct Educator

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To decide if the point (0,0) satisfies the inequality y<2x+3 we need to start by substituting those values in for the x and y in the equation.

(0)<2(0)+3

0<0+3

0<3

We see that the solution is 0<3 (0 is less than 3).

Since we know that this statement is true, we then know that the point (0,0) satisfies our inequality.

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lritchey7 | Middle School Teacher | (Level 1) Adjunct Educator

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A linear inequality describes an area of the coordinate plane that has a boundary line. Every point in that region is a solution of the inequality. 
In simpler speak, a linear inequality is just everything on ONE side of a line on a graph.

There are a couple ways to determine whether the point (0,0) lies in the region described by the inequality, y < 2x + 3.

You could graph the inequality on a coordinate plane.  However, the easiest way is by using substitution.

To do this take the and y values from the ordered pair and substitute them into the inequality.  Remember an ordered pair is always written (x,y).  In this case = 0 and y = 0.

STEPS:

0 < 2(0) + 3            0 is substituted for both the x and y values.  

0 <  3                     Next, simplify the expression on the right using the order                               of operations (multiplication first, then addition).

Since 0 < 3 is a true statement, the ordered pair (0,0) satisfies the inequality, y < 2x + 3.  

kspcr111's profile picture

kspcr111 | In Training Educator

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Given

y < 2x + 3; (x,y)= (0,0)

to find whether (0,0) satisfies the inequality or not

sol:

By substituting (0,0) we will get to know whether it  satisfies the inequality.

y < 2x + 3;  (0,0)

=> 0< 2(0)+3

=> 0 < 3    : True

So, (0,0) satisfies the inequality y<2x+3

jennldean's profile pic

jennldean | eNotes Newbie

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To determine if any set of given points satisfies an equation, you must substitute the points in for x and y in the equation.

Determine if (0,0) satisfies the inequality: 

(x,y)

(0,0)

0 < 2(0)+3

0<0+3

0<3

So, (0,0) does satisfy the equation. 

mspowell's profile pic

mspowell | eNotes Newbie

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In order to determine if (0, 0) satisfies the inequality

y < 2x + 3

you must first substitute the 2 values into the inequality.  

An ordered pair is always (x, y), so x = 0 and y = 0

First try putting those values into the inequality.

0 < (2*0) + 3

Now work the multiplication first (due to order of operations).

0 < 0 + 3

Now do the addition.

0 < 3

Ask yourself, is 0 less than 3?  Yes it is!

Therefore, (0, 0) will, in fact, satisfy the inequality.

s314-moehle's profile pic

s314-moehle | eNotes Newbie

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Since (0, 0) represents the x and y value for an ordered pair (x, y) on a coordinate plane, substitute the values for the inequality to see whether or not it is a solution.

y < 2x +3

0 < 2(0) + 3

0 < 0 + 3

0 < 3. True  So (0, 0) is a solution.

nisarg's profile pic

nisarg | Student, Grade 11 | (Level 1) Valedictorian

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 Determine whether (0, 0) satisfies each inequality.'

any point on a coordinate plain is an (X,Y) point so using (0,0) x=0 and y=0

so you need to replace the X and Y in  

so 0<2(0)+3

0<0+3

0<3

there fore the coordinate 0,0 works in this equation to make it true  i hope this is helpful

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