Multiplying Equations

Solving Systems Multiply Both Equations

By Scott Donnelly

Multiple Choice

What is the LCM of 4 and 6?

• 12

• 24

• 48

• 6

Multiple Choice

Which variable should you eliminate in the system below?

$$2x-5y=15$$  

$$3x+5y=25$$  

• x

• y

Open Ended

Why should we eliminate the y variable?

$$2x-5y=15$$  

$$3x+5y=25$$  

Solving System by Elimination

​Steps

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

   2. Multiply each term in the equation to get the LCM for the first equation and second equation

3. ​Use SSS or DSA to eliminate.

4. Solve for the remaining variable.

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

6. Write the answer as an ordered pair.

Poll

Which variable do you want to eliminate?

• x

• y

Solve System

Poll

Which variable do you want to eliminate?

• x

• y

Poll

Which variable do you want to eliminate?

$$3x+5y=12$$  

$$-2x+3y=-8$$  

• x

• y

Draw

What is the LCM of the variable you want to eliminate

$$3x+5y=12$$  

$$-2x+3y=-8$$  

Draw

Multiply the first equation to get the same coefficients.

$$3x+5y=12$$  

$$-2x+3y=-8$$  

Draw

Multiply the second equation to get the same coefficients.

$$3x+5y=12$$  

$$-2x+3y=-8$$  

Draw

Use DSA or SSS to solve for a variable.

$$3x+5y=12$$  

$$-2x+3y=-8$$  

Draw

Solve for the other variable

$$3x+5y=12$$  

$$-2x+3y=-8$$