Solve Linear Systems by Multiplying

System of Equations 1 Multiplication

By Scott Donnelly

​Least Common Multiple

Video below shows how to find LCM.

https://www.youtube.com/watch?v=Z6-LksV08qU&t=88s

Multiple Choice

What does DSA stand for?

• Don't Subtract Add

• Distribute Signs Always

• Different Signs Add

Same

Sign

Subtract​

​SSS

Different

Signs

Add​

​DSA

Solving Systems

Multiple Choice

On the system below, are we going to add or subtract?

$$3x+4y=12$$  

$$2x+4y=8$$  

• Add

• Subtract

Multiple Choice

After subtracting what will the new equation look like?

$$3x+4y=12$$  

$$2x+4y=8$$  

• $$5x=20$$  

• $$1x=4$$  

• $$5x=4$$  

• $$1x=20$$  

Math Response

Solve for x

$$3x+4y=12$$  

$$2x+4y=8$$  

Type answer here

Correct Answer: 4

Deg^°

Rad

Math Response

Solve for y

$$3x+4y=12$$  

$$2x+4y=8$$  

Type answer here

Correct Answer: 0

Deg^°

Rad

Fill in the Blanks

Write answer as ordered pair.

$3x+4y=12$  

$2x+4y=8$  

Solving by Elimination

Without simple elimination, bold is new step

1. Line of the terms, x over x, y over y and number after equal sign.

2. Look for opposite coefficients or the same coefficient.

   1. ​Use LCM of the coefficients to create same or opposite. We try to only multiply 1 equation if we can

3. ​Use SSS or DSA to eliminate.

4. Solve for remaining variable.

5. Substitute back into original equation to solve for other variable.​

1. LCM of 2 and 3 is 6, but LCM of 1 and 2 is 2.

2. Going to multiply bottom equation by 2

3. Then use DSA to solve

4. Substitute back into original equation

Example

Solving by Elimination

Multiple Choice

Which variable should you eliminate?

$$x+4y=7$$  

$$4x-3y=9$$  

• x

• y

Fill in the Blanks

What is the least common multiple of 1 and 4

$x+4y=7$  

$4x-3y=9$  

Multiple Choice

Which equation should you multiply by 4?

$$x+4y=7$$  

$$4x-3y=9$$  

• $$x+4y=7$$  

• $$4x-3y=9$$  

• Both

Multiple Choice

When you multiply the top equation by 4, what will new equation become?

$$x+4y=7$$  

$$4x-3y=9$$  

• $$4x+4y=7$$   

• $$4x+16y=7$$   

• $$4x+16y=28$$   

Multiple Choice

Are you going to add or subtract the new equations?

$$4x+16y=28$$   

$$4x-3y=9$$  

• Add  

• Subtract  

Math Response

What will equation look like after you subtract?

$$4x+16y=28$$   

$$4x-3y=9$$  

Type answer here

Correct Answer: 19y=19

Deg^°

Rad

Math Response

Solve for y

$$4x+16y=28$$   

$$4x-3y=9$$  

Type answer here

Correct Answer: y=1

Deg^°

Rad

Math Response

Solve for x

$$x+4y=7$$   

$$4x-3y=9$$  

Type answer here

Correct Answer: 3

Deg^°

Rad

Draw

Solve the System, on dry erase board, write answer as ordered pair on here.

$$2x-3y=1$$  

$$x+2y=-3$$