Systems of Equations

Presentation

•

Mathematics

•

8th - 11th Grade

•

Medium

•

CCSS

8.EE.C.8B, HSA.REI.C.6

Standards-aligned

Krista Simonsen

Used 17+ times

FREE Resource

17 Slides • 19 Questions

Systems of Equations

by Krista Simonsen

When 2 lines are drawn on the same graph, there are 3 possible outcomes.

The lines intersect
The lines don't intersect
The lines are on top of each other

Multiple Choice

Here is an example of 2 lines being graphed. What answer choice matches the situation shown?

The liness intersect

The lines do not intersect

The lines are on top of each others

For lines not to intersect at all...

The lines must be parallel
If the lines are parallel, we can write 'NO SOLUTION'
Parallel lines have the SAME SLOPE but DIFFERENT y-intercepts

Multiple Choice

Here is an example of 2 lines being graphed. What answer choice matches the situation shown?

The liness intersect

The lines do not intersect

The lines are on top of each others

For lines to be right on top of one another...

You should only see one line even though there are 2 equations.
When this situation occurs, you can write "INFINITE SOLUTIONS"
The 2 equations have to be mathematically the equal to one another for the lines to be on top of one another.

Multiple Choice

Here is an example of 2 lines being graphed. What answer choice matches the situation shown?

The liness intersect

The lines do not intersect

The lines are on top of each others

For lines to intersect once...

The place where the line intersects is at an ordered pair
Write the orderd pair in the form of (x,y).
The slopes of the two lines must be different.

Multiple Choice

What is the point of intersection for the problem at the left, if any?

(4,2)

(-2,1)

No Solution

Infinite Solutions

Multiple Choice

What is the point of intersection for the problem at the left, if any?

(4,2)

(-2,1)

No Solution

Infinite Solutions

Multiple Choice

What is the point of intersection for the problem at the left, if any?

(4,2)

(-2,1)

No Solution

Infinite Solutions

Multiple Choice

What is the point of intersection for the problem at the left, if any?

(1,-4)

(-1,-4)

(-4,1)

(-4,-1)

Solving Systems of Linear Equations by Substitution

Step #1 Isolate a variable in one of the equations to get an expression

Solving Systems

Steps #2 Substitute that expression (from step #1) into the other equation.

Solving Systems

Step #3 Solve for the intersection point (x , y).

Solving Systems

step #4 write your answer as an order pair (x, y).

Multiple Choice

The solution to a system of equations is any ordered pair that makes both equations true.

TRUE

FALSE

Multiple Choice

Solve the following system:

$y=-2$

$4x-3y=18$

$\left(3,\ -2\right)$

$\left(3,\ 2\right)$

$\left(-2,3\right)$

$\left(2,\ 3\right)$

Multiple Choice

Solve this system by substitution.

(1, -4)

(1, 4)

(-4, -7)

(-7, -4)

Multiple Choice

Solve the systems by substitution:

x = -4y

x - y = 15

(-3, 12)

(12, 3)

(3, 12)

(12, -3)

Multiple Choice

Which of the following correctly shows substituting the first equation into the second equation?

y = 9(2x + 10) - 2

9x - 2 = 3x + 10

Multiple Choice

Which of the following correctly shows substituting the first equation into the second equation?

5x = -x + 4

5(y + 4) + 6y = 13

5x + 6(-x + 4) = 13

5x + (-x + 4) = 13

Multiple Choice

Which of answer shows the correct steps to solve for x?

$-3x+4\left(3x-5\right)=7$ $-3x+12x-5=7$ $9x-5=7$ $9x=12$ $x=1.25$

$-3\left(3x-5\right)+4x=7$ $-9x+15+4x=7$ $-5x+15=7$ $-5x=-8$ $x=1.6$

$-3x+4\left(3x-5\right)=7$ $-3x+12x-20=7$ $9x-20=7$ $9x=27$ $x=3$

$-3x+4\left(3x-5\right)=7$ $-3x+12x-15=7$ $9x-15=7$ $9x=9$ $x=1$

***VERY IMPORTANT SLIDE***

Multiple Choice

I can combine 2 linear equations if the coefficients are not opposites.

True

False

SYSTEMS OF EQUATIONS ARE 2 EQUATIONS WITH 2 VARIABLES

One way to solve them is by ELIMINATING one of the variables

Multiple Choice

Which variable has opposite coefficients?

Multiple Choice

Which variable can we ELIMINATE?

$5x\ +\ 8y\ =\ 23$ $-5x\ +\ 4y\ =\ 5$

WHEN SOLVING USING ELIMINATION

Look for opposite coefficients
IF THERE IS NONE, MULTIPLY EVERY TERM IN AN EQUATION

Multiple Choice

Solve by elimination -2x + 6y = 16 -4x - 3y = 2

(2,2)

(-2, -2)

(-2,2)

(2,1)

Multiple Choice

Solve for x and y 3x + 2y = 16 7x + y = 19

(-2,5)

(-2,-5)

(2,-5)

(2,5)

Systems of Equations

by Krista Simonsen

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