Systems of Equations and Inequalities Review

Systems of Equations

Multiple Choice

Review: Which inequality matches the graph shown?

• y < x - 2

• y > 2x - 1

• y > x - 2

• y > x - 2

​If the system has a solution, it will be the ordered pair where the point of intersection occurs.

​Solve by Graphing

​Solution: (3,0)

Multiple Choice

Solve the following system by graphing.  What is the solution?

• Infinite number of solutions
• (3, 3)
• (3, -3)
• (-3, 3)

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Multiple Choice

What is the solution to the system?

• (6, 8)
• (8, 6)
• (-6, 8)
• No solution

Multiple Choice

How many solutions does this system have?

y = 8x + 8

y = 8x + 8

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

How many solutions does this system have?

y = 7x - 3

y = 7x +6

• One Solution

• No Solution

• Infinitely Many Solutions

Solving System of Equations Substitution

​Step 1: Isolate a variable
Step 2: Substitute
Step 3: Solve
Step 4: Substitute

​Let's try one together...

Step 1:
Isolate a
variable

Multiple Choice

Isolate the y to equation $$x+y=-2$$

• $$y=x+2$$

• $$y=x-2$$

• $$y=-x-2$$

• $$y=-x+2$$

​Let's try one together...

​Step 2: Substitute the expression into the second expression

Hotspot

Knowledge Check: Where will I substitute the new equation?

​Let's try one together...

​

​Step 3: Solve the new equation

Steps for elimination method :

• Step 1: Align your variables

• Step 2: Identify variables with equal and opposite coefficients (example: -2x and 2x)

• Step 3: Add/ subtract equations (vertically)

• Step 4: Solve for the other variable

Multiple Choice

what is the variable that willl be "eliminated"?

5x - 4y = 11

5x + 4y = -14

• x variable

• y variables

• both variables

Multiple Choice

2x - 6y = 20

2x + 5y = -11

what would the top equation become when you multiply everything by -1?

• 2x - 6y = 20

• -2x - 6y = -20

• -2x + 6y = 20

• -2x + 6y = -20

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

Math Response

Solve for x.

$$4x-\left(-x-2\right)=-3$$

(just the number)

Type answer here

Correct Answer: -1

Deg^°

Rad

​Let's try one together...

​

​Step 4: Substitute the known variable into either equation to solve for the other variable.

Math Response

After substitution, what would be the new equation for y?

Type answer here

Correct Answer: y=-\left(-1\right)-2

Deg^°

Rad

​Let's try one together...

​

​Solution (-1, -1)

Review of Graphing Linear Inequalities

• Change to Slope-Intercept Form if needed (Get y by itself).

• Plot y intercept and use the slope to find the second point.

• Determine if dashed or solid line (< , > is dashed and < , > is solid).

• Determine whether to shade above or below ( > shade above, < shade below).

Multiple Choice

Review: Which inequality matches the graph shown?

• y < x - 2

• y > 2x - 1

• y > x - 2

• y > x - 2

Steps to Graphing Systems of Inequalities

• Make sure both inequalities are in Slope-Intercept Form.

• Graph both inequalities (Don't forget to determine dashed or solid line and shade above or shade below).

• Heavily shade in the portion where the shaded regions overlap. This is the solution to the system of inequalities.

• At this point, downsize this screen and go watch the video that is also attached on Google Classroom and then come back here for the practice problems.

Solution to a System of Inequalities

Is all ordered pairs that make ALL inequalites true.

**WHERE THE SHADED PORTIONS OF THE BOTH INEQUALITIES OVERLAP.**

We will start by graphing.

Multiple Select

To graph:

$$y\ge x+1$$

Select all that apply.

• y-intercept = 1
  
  slope = 1

• solid line
  

• dotted line

• shade above

• shade below

Multiple Select

To graph:

$$y<3x-2$$

Select all that apply.

• y-intercept = -2
  
  slope = 3

• solid line
  

• dotted line

• shade above

• shade below

Let's make them a system!

Graph both inequalities on the same coordinate plane

But wait...where is the solution?!

Poll

Where do you think the solution will be?

• Blue

• Purple

• Red

• White

• All of blue and all of red