Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
2nd Edition
ISBN: 9780076602919
Author: McGraw-Hill Education
Publisher: McGraw-Hill Education
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Question
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Chapter 2.4, Problem 41PPS

(a)

To determine

Make a table for y=2x+4 and y=−x−2 . Graph the ordered pairs from the table.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The equations y=2x+4 and y=−x−2

Concept Used:

To make a table, first choose some values of x and find the corresponding y values according to the equation.

The equations y=2x+4 and y=−x−2

Calculation:

Table for equation y=2x+4

    xy=2x+4(x,y)
    − 2 y=2(−2)+4y=−4+4=0(−2,0)
    0y=2(0)+4y=0+4=4(0,4)
    − 3 y=2(−3)+4y=−6+4=−2(−3,−2)

Table for equation y=−x−2

    xy=−x−2(x,y)
    − 2 y  =  −  (−2)  −  2 y  =  2 − 2 = 0 (−2,0)
    0y  =  0  −  2 y  =   − 2  (0,−2)
    − 6 y  =  −  ( − 6)  −  2 y  =   6  −  2  =  4  (−6,−4)

Graph:

  Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1), Chapter 2.4, Problem 41PPS

Thus, we can see in the table and the graph both that the intersection point of the graphs is (−2,0)

(b)

To determine

To find the value of x from the equations y=2x+4 and y=−x−2

(b)

Expert Solution
Check Mark

Answer to Problem 41PPS

  (  −  2  ,  0  )

Explanation of Solution

Given:

The equations y=2x+4 and y=−x−2

Concept Used:

To solve the equation we can use the substitution method. Substitute y=2x+4 to the second equation y=−x−2

Calculation:

The equations y=2x+4 and y=−x−2

Substitute y=2x+4 to the second equation y=−x−2

Now we get the equation: 2x+4=−x−2

           2x+4=−x−2     2x  +x  +4  =  −x  +  x  −  2 [ Add  x  to  both  sides ]          3x    +    4    =    −2          3x    +    4    − 4    =    −2    −  4  [ Subtract  4  from  both  sides ]           3x    =    −6          3x3    =    −63    [ Divide  both  sides  by  3]             x    =    −  2

  y  =  2x+4  ;   y  =   2  (−2)  +  4y  =  −4  +  4  =  0 x  =  −2  ;  y  =  0  

  y  =  −x−2  ;   y  =   −  (−2)  −  2y  =  2  −  2  =  0 x  =  −2  ;  y  =  0

Thus, the solution of both the equation is (  −  2  ,  0  )

(c)

To determine

Explain how we get the solution of the equations y=2x+4 and y=−x−2 from Part’ a ‘ and Part ‘ b ‘

(c)

Expert Solution
Check Mark

Answer to Problem 41PPS

  (  −  2  ,  0  )

Explanation of Solution

Given: the equations y=2x+4 and y=−x−2

Concept Used:

In the Part a, in the tables for the equations y=2x+4 and y=−x−2 , we can see that the point (  −  2  ,  0  ) is common in both the tables.

In the graph also we can observe that the intersection point is (  −  2  ,  0  ).

We know that according to the theory for a system of equation, the intersection of two lines is the solution of the equations.

In the part b, we have solved the equation by substitution method and got the same solution.

Thus, we can say that the solution of the equations is (  −  2  ,  0  ) from part ‘a’ and part ‘b’

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Chapter 2.4, Problem 40PPS
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Chapter 2.4, Problem 42HP

Chapter 2 Solutions

Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)

Ch. 2.1 - Prob. 1AGPCh. 2.1 - Prob. 1BGPCh. 2.1 - Prob. 2GPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4AGPCh. 2.1 - Prob. 4BGPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 1CYUCh. 2.1 - Prob. 2CYUCh. 2.1 - Prob. 3CYU
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Prob. 9MCQCh. 2 - Prob. 10MCQCh. 2 - Prob. 11MCQCh. 2 - Prob. 12MCQCh. 2 - Prob. 13MCQCh. 2 - Prob. 14MCQCh. 2 - Prob. 15MCQCh. 2 - Prob. 16MCQCh. 2 - Prob. 17MCQCh. 2 - Prob. 18MCQCh. 2 - Prob. 19MCQCh. 2 - Prob. 20MCQCh. 2 - Prob. 21MCQCh. 2 - Prob. 22MCQCh. 2 - Prob. 23MCQCh. 2 - Prob. 24MCQCh. 2 - Prob. 25MCQCh. 2 - Prob. 1SGRCh. 2 - Prob. 2SGRCh. 2 - Prob. 3SGRCh. 2 - Prob. 4SGRCh. 2 - Prob. 5SGRCh. 2 - Prob. 6SGRCh. 2 - Prob. 7SGRCh. 2 - Prob. 8SGRCh. 2 - Prob. 9SGRCh. 2 - Prob. 10SGRCh. 2 - Prob. 11SGRCh. 2 - Prob. 12SGRCh. 2 - Prob. 13SGRCh. 2 - Prob. 14SGRCh. 2 - Prob. 15SGRCh. 2 - Prob. 16SGRCh. 2 - Prob. 17SGRCh. 2 - Prob. 18SGRCh. 2 - Prob. 19SGRCh. 2 - Prob. 20SGRCh. 2 - Prob. 21SGRCh. 2 - Prob. 22SGRCh. 2 - Prob. 23SGRCh. 2 - Prob. 24SGRCh. 2 - Prob. 25SGRCh. 2 - Prob. 26SGRCh. 2 - Prob. 27SGRCh. 2 - Prob. 28SGRCh. 2 - Prob. 29SGRCh. 2 - Prob. 30SGRCh. 2 - Prob. 31SGRCh. 2 - Prob. 32SGRCh. 2 - Prob. 33SGRCh. 2 - Prob. 34SGRCh. 2 - Prob. 35SGRCh. 2 - Prob. 36SGRCh. 2 - Prob. 37SGRCh. 2 - Prob. 38SGRCh. 2 - Prob. 39SGRCh. 2 - Prob. 40SGRCh. 2 - Prob. 41SGRCh. 2 - Prob. 42SGRCh. 2 - Prob. 43SGRCh. 2 - Prob. 44SGRCh. 2 - Prob. 45SGRCh. 2 - Prob. 46SGRCh. 2 - Prob. 47SGRCh. 2 - Prob. 48SGRCh. 2 - Prob. 49SGRCh. 2 - Prob. 50SGRCh. 2 - Prob. 51SGRCh. 2 - Prob. 52SGRCh. 2 - Prob. 53SGRCh. 2 - Prob. 54SGRCh. 2 - Prob. 55SGRCh. 2 - Prob. 56SGRCh. 2 - Prob. 57SGRCh. 2 - Prob. 58SGRCh. 2 - Prob. 59SGRCh. 2 - Prob. 60SGRCh. 2 - Prob. 61SGRCh. 2 - Prob. 62SGRCh. 2 - Prob. 63SGRCh. 2 - Prob. 64SGRCh. 2 - Prob. 65SGRCh. 2 - Prob. 66SGRCh. 2 - Prob. 67SGRCh. 2 - Prob. 68SGRCh. 2 - Prob. 69SGRCh. 2 - Prob. 70SGRCh. 2 - Prob. 71SGRCh. 2 - Prob. 72SGRCh. 2 - Prob. 73SGRCh. 2 - Prob. 74SGRCh. 2 - Prob. 75SGRCh. 2 - Prob. 76SGRCh. 2 - Prob. 77SGRCh. 2 - Prob. 78SGRCh. 2 - Prob. 79SGRCh. 2 - Prob. 1PTCh. 2 - Prob. 2PTCh. 2 - Prob. 3PTCh. 2 - Prob. 4PTCh. 2 - Prob. 5PTCh. 2 - Prob. 6PTCh. 2 - Prob. 7PTCh. 2 - Prob. 8PTCh. 2 - Prob. 9PTCh. 2 - Prob. 10PTCh. 2 - Prob. 11PTCh. 2 - Prob. 12PTCh. 2 - Prob. 13PTCh. 2 - Prob. 14PTCh. 2 - Prob. 15PTCh. 2 - Prob. 16PTCh. 2 - Prob. 17PTCh. 2 - Prob. 18PTCh. 2 - Prob. 19PTCh. 2 - Prob. 20PTCh. 2 - Prob. 21PTCh. 2 - Prob. 22PTCh. 2 - Prob. 23PTCh. 2 - Prob. 24PTCh. 2 - Prob. 25PTCh. 2 - Prob. 1CRCh. 2 - Prob. 2CRCh. 2 - Prob. 3CRCh. 2 - Prob. 4CRCh. 2 - Prob. 5CRCh. 2 - Prob. 6CRCh. 2 - Prob. 7CRCh. 2 - Prob. 8CRCh. 2 - Prob. 9CRCh. 2 - Prob. 10CRCh. 2 - Prob. 11CRCh. 2 - Prob. 12CRCh. 2 - Prob. 13CRCh. 2 - Prob. 14CRCh. 2 - Prob. 15CR

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