Topic 4 Represent and Solve Equations

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

y=4x+1

2y-3x=12

• (2,9)

• (9,2)

• There are infinitely many solutions

• 2)There is no solution.

y=2x+9

y=9x+10

• (3,4)

• (-1/7,61/7)

• There are infinitely many solutions.

• No soulution

What is the Substitution Method

What is the first step to solving an system of equations

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.

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

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

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)

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

x + 2y = 14

y = 3x – 14