Solving Systems of Equal Value

EML - Systems of Equations Review

Review of the last Unit 4 in Algebra 1.

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There Are Four Ways of Solving Systems of Equations:

• Elimination Method

• Substitution Method

• Graphing Method

• Equal Values

Elimination Method

The elimination method is best used when we have two variables with opposite sign coefficients. For example:

 $4x\ +\ 2y\ =\ 20$  
 $-\ x\ +\ y\ =\ 10$  

Multiple Choice

what is the resulting combined equation to the following system:

5x - 4y = 11

5x + 4y = -14

• 5x = -3

• 10y = -3

• 10x = -3

• 10x = -25

Multiple Choice

what is the variable that willl be "eliminated"?

5x - 4y = 11

5x + 4y = -14

• x variable

• y variables

• both variables

Subsitution Method

The substitution method is best used when we have a system written in terms of x or y (or other variables). For example:

 $y\ =\ 2x\ +\ 10$  
 $-\ x\ +\ y\ =\ 10$  

Multiple Choice

Solve:

y = 7x + 7

2y + 2x = -18

• (5, 0)

• (9, 18)

• (-2, -7)

• (1, 16)

Multiple Choice

Solve:
x = -3y - 17
2x + 3y = -7

• (1, -20)
• (3, 0)
• (-5, -2)
• (10 , -9)

Graphing Method

We generally will be able to graph our system of of equations. The intersection of the graph will be the solution to our system. Generally, the only time we do not want to graph our system is if we are unable to determine the exact value since it is a fraction or a decimal. 

Multiple Choice

What is the solution?

• (6, 3)
• (3, 6)
• (-6, 3)
• No solution

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Equal Values

We can solve for the equal values if both equations are equal to the same variable. If they are, then we can easily set the two equations in the system equal to each other and solve. This was also useful in word problems where we want to find where two points will be the same. 

Multiple Choice

What is the solution to the system of equations? 
y = 3x - 8
y = 4 - x

• (3,1)
• (1,3)
• (-3,1)
• (3,-1)

Multiple Choice

Solve the system of equations by equal values.

y = -4x + 5

y = 3x - 16

• (-3, -25)

• (3,-7)

• (11, 17)

• (21, 47)

Word Problem Practice

Sysems of Equations

Multiple Choice

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32
  1z = 0.75
• 5q + 2z = 1.32
  3q + 1z = 0.75
• q + z = 1.32
  q + z = 0.75
• 5q + 2z = 0.75
  3q + 1z = 1.32

Multiple Choice

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Multiple Choice

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  How many nickels and dimes did Dennis earn? 

• 40 nickels, 40 dimes
• 52 nickels, 28 dimes
• 28 nickels, 52 dimes
• 30 nickels, 50 dimes

Multiple Choice

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used? 

• 1s + 3c = 38
  2s + 3c = 52
• 3s + 1c = 38
  3s + 2c = 52
• s + c = 38
  s + c = 52
• 3s + 3c = 38
  1s + 2c = 52

Multiple Choice

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2
• x = -2 
  y = 5
• x + y = -2
  x - y = -10
• x + y = -10
  x - y = -2

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