Systems of linear Equations and Inequalities

Graphing Systems of Equations

100

When two lines on the graph are parallel , what solution is that?

It’s a No solution or The system has no solution 

200

If two lines on the graph overlap each other , what does that mean?

It means that there is Infinite solution.

300

Graph : y = 2x - 3 and y = -x + 3.

where does the line intersect?

It Intersect at ( 2 , 1)

400

Graph. Y = -2x + 6 , x + y = 4.

( 2,2)

500

Create a system with one solution. : must show explanation and answer. ( must be different examples from mine)

Example : i take these two equations ( 5x + 2y =12 and 3x - y = 0) and which i put into Desmos and they intersect at (1.09 , 3.2). I know it’s one solution since the graph intersects and gives me one pair.

Substitution

100

What’s the first step in substitution?

The first step is to solve one equation for on variable 

200

Solve : y = 2x. and x + y = 12.

X + 2x = 12 > 3x = 12 > x == 4, y = 8.

so the answer is ( 4.8)

300

Solve : y = -x + 5. And 2x + y =7.

2x + (x + 5) = 7 , x +5 = 7

400

Solve. y = 2x - 5 , 3x + y = 10.

x will equal to 3 , x will equal to 1 ( 3,1)

500

Solve. X = 2y + 1 , 3x - y = 14.

x will equal to 5.4 or 27/5. y will equal to 2.2 or 11/5.

Elimination(addition and subtraction)

100

If both variables cancel , what does that mean?

it means there’s no solution to the problem.

200

Solve. x + y = 10 And x - y = 4.

( x + y ) + ( x - y ) = 2x = 14 which equals to 7.

300

Solve. 2x + y = 9 and - 2x + y = 1.

x equals to 2. Y equals to 5. ( x = 2 , y = 5)

400

Solve. 1/2x + y = 5. and 1/2x - y = 1.

x = 6. , y = 2.

500

Solve. 5x + 3y = 24, 5x - 2y = 9.

y = 3, x = 3 ( 3,3)

Elimination(multiplication)

100

What if you multiplied both equations and it turns to be the same answer? What does that mean?

It means theres many solutions or As we call it, Infinitely solutions

200

True/False. you can use elimination if the coefficients match.

false because we can multiply to make them match.

300

True/false. When the final elimination is ( 0 = 4) , does it mean there’s no solution?

True.

400

Solve. -9x + 3y = 27 

           -3x + 4y =27

( -1, 6): x is -1 , y is 6.

500

Solve. 10x + 12y = -26

         -6x + 6y = -24

( 1, -3): x is 1 , y is -3

Systems of Inequalities

100

True or false : The solution to a system of inequalities is always a line.

False. Because its a region.

200

Graph. Y > -3/4x + 4 

           y > 1/2x - 1.  ( what points are on the graph)

(4,1)

300

Graph. 2x + 3y ~> -9

           X ~< -3 ( what points are on the graph)

(-3,0) or ( -3,-1)

400

Graph .  Y ~> 1/3 x + 3 

             Y > 2x-2. ( what points are on graph)

( 3, 4 )

500

Graph. -x + 3y ~< -6

           -5 + 3y ~< 6 ( what points are on the graph )

(0,-2)