Topic 4

Whats the definition of a solution of a system of linear equations.

• the point at which the lines representing the linear equations intersect.

• A system of linear equations is a set of two linear equations with two variables

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

y=4x+1

2y-3x=12

• (2,9)

• (9,2)

• There are infinitely many solutions

• 2)There is no solution.

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

y=2x+9

y=9x+10

• (3,4)

• (-1/7,61/7)

• There are infinitely many solutions.

• No soulution

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What is the Substitution Method

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.7

What is the first step to solving an system of equations

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

Which of the following gives a valid reason for using the given solution method to solve the system of equations shown?

Equation I: 4x − 5y = 4

Equation II: 2x + 3y = 2

• Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.

• Substitution; Equation I can be solved for x in one step by dividing both sides by 4.

• Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation

• Substitution; Equation II can be solved for x in one step by subtracting 3y from both sides.

Tags

CCSS.HSA.REI.C.6

Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Choose the system of equations that models the situation.

• 2x + 3y = 7.20

  2x + 4y = 8.80

• 3x + 2y = 7.20

  4x + 2y = 8.80

• 2x + 3y = 7.20

  4x + 2y = 8.80

• 2x + 3y = 8.80

  4x + 2y = 7.20

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable?

5x + 6y = 18

2x – 3y = 12

Tags

CCSS.HSA.REI.C.6

Use substitution to determine the solution of the system of equations.

y = −2x − 7

2y − x = 1

• (−1,0)

• (21/2,−28)

• (−6,−5/2)

• (−3,−1)

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

Use substitution to determine the solution of the system of equations. Write the solution as an ordered pair.

x + 2y = 14

y = 3x – 14

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11