Systems of Linear Equations Day 2 Substitution & Addition

Systems of Equations

Solving by Substitution & Addition

1.2.5

Target: To Improve our Skills in Using Substitution to Solve Linear Systems AND to Start Learning How to Use Elimination.

​Review from Yesterday

Multiple Choice

A ________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

Multiple Choice

The ordered pair that satisfies all equations in the system.

• system of equations

• function

• graph

• solution of a system

Multiple Choice

Is $$\left(1,\ 2\right)$$ a solution to the system $$x+y=3$$ & $$3x-y=1$$

• Yes

• No

Multiple Choice

Is $$\left(-2,\ -3\right)$$ a solution to the system $$x-2y=-2$$ & $$3x-2y=6$$

• Yes

• No

Multiple Choice

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

Multiple Choice

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

• (0, -1.5)

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

​Go to Lecture Notes

Solving Using Substitution (link)

Variable Already Isolated (Reference Page Link)

Fill in the Blank

Q12 - Solve the System

$$2x-y=9\ \&\ x=y+1$$

Answer as an ordered pair

Fill in the Blank

Q13 - Solve the System

$$7x-y=-15\ \&\ y=2x$$

Answer as an ordered pair

Open Ended

Q15 - Solve the System

$$x+3y=6\ \&\ 2x+3y=10$$

Answer as an ordered pair

Fill in the Blank

Q16 - Solve the System

$$5x+3y=-9\ \&\ -2x+y=8$$

Answer as an ordered pair

Multiple Choice

Q18 - Solve the System

$$\frac{1}{4}x-y=2\ \&\ x=4y+8$$

Answer as an ordered pair

• Independent Solution

• No Solution

  ∅

• Dependent Solution

  $$\left(x,\ \frac{1}{4}x-2\right)$$

• Dependent Solution

  $$\left(x,\ 4y+8\right)$$

Multiple Choice

Q19 - Solve the System

$$4x-3y=12\ \&\ -8x+6y=-30$$

Answer as an ordered pair

• Independent Solution

• No Solution

  ∅

• Dependent Solution

  $$\left(x,\ \frac{4}{3}x-4\right)$$

• Dependent Solution

  $$\left(x,\ \frac{4}{3}x-12\right)$$