Solving Systems with Elimination

Solve a system of equation using Elimination (Day 2)

by Kristin Parsons

Multiple Choice

To solve a system of equation using the Elimination method, you first need to line up the equations so the matching terms are in the same order.

The next step is to__________________?

• Get the equation into slope-intercept form.

• Get x or y by itself.

• Look for the term with the same coefficient and add or subtract.

• Substitute the expression in for either x or y.

• I have no idea what the next step is.

Practice: Solve the System of equation using Elimination / Combination Method.

​

​Look for the term with a coefficient are the same (1y)

2x + 5y = 17

                                    6x – 5y = -9

​ ​

Combine like terms to eliminate the y term.

​Solve for x

​Substitute the value for x into the original equation(s) to find the y value.

​Enter the solution on the next slide. (x, y)

Multiple Choice

Solve the System of Equation

2x - 3y = 23

x + 3y = -20

• (3, -7 2/3)

• (1, -7)

• x = 43

• (-7, 1)

Multiple Choice

If I want to solve using Elimintion Method what might I do to eliminate the x terms?

2x + 8y = 6

5x + 20y = 15

• Multiply the first equation by 5 and the second by 2 to change the x term to 10x for both.

• Solve for x in one equation, then substitution the expression with y into the other equaiton

• Multiply the y terms to a common multiple of 8 and 20.

• Subtract the second equation from the first.

Example: ​Solve using Elimination Method, coefficients are not the same

​7x - y = 19 -> 3(7x - y = 19) -> 21x - 3y = 57

​2x - 3y = 19 -> -1 ( 2x - 3y= 19) -> -2x + 3y = -19

​ 19x = 38 (divide both sides by 19)

​ x = 2

​7(2) - y = 19

​14 - y = 19

​- y = 5

​ y = -5

​

(2, -5)