Solving Linear Systems Algebraically

Solving a System of Equations Algebraically

Let's look at this puzzle quickly...

Methods to solve:

• Graphing

• Substitution

• Elimination

• Calculator

Graphing

We have already done this.

Substitution

• This is the method we will mostly use.

• We get one variable by itself and then we SUBSTITUTE it's value into another equation with matching variables.

• It is much easier to understand with a visual representation.

Elimination

• Elimination can be the easiest way to solve systems.

• The problem is that you must have the two equations in the exact same form.

• This takes a bit of time to get the hang of, but once you do it can be so very easy to solve.

• You still need to substitute at the end, so it doesn't save that step.

Multiple Choice

Solve the given system by using substitution method.

• Infinite number of solutions

• x = 0, y = 7

• x = -5, y = -7

• x = 5, y = 7

• no solution

Multiple Choice

Using Substitution, solve for the following system of linear equations:  $$y=2x+1$$  

$$x+y=16$$  

• (3,-7)

• No solutions

• Infinitely many solutions

• (5,11)

Multiple Choice

Using Substitution, solve for the following system of linear equations:

y = 2x + 5

y = 4x + 9

• (-2, 1)

• (-2, -1)

• (2, -1)

• (2, 1)

Multiple Choice

Solve the given system by using substitution method:

x = 3y -13

4x + 2y = 4

• x = 1, y = 4

• x = -1, y = -4

• x = -1, y = 4

• x = 1, y = -4

Multiple Choice

Use elimination method to solve the system below.

4x + 8y = 20

-4x + 2y = -30

• (-7,1)

• (2,-5)

• (-2,5)

• (7,-1)

Multiple Choice

Solve by elimination:

4x + 4y = 4

3x + 4y = 10

• x = 7,y = -6

• x = -6, y = 7

• x = 6, y = 7

• x = 7, y = 6

Multiple Choice

Solve by elimination:

2x + 9y = -7

6x - 3y = 9

• (-1, -1)

• (2,-1)

• (1,1)

• (1,-1)

Multiple Choice

Using the elimination method, determine the solution to the system below.

x - y = 11

2x + y = 19

• x = 10, y = -1

• x = -1, y = 10

• x = 3, y = -4

• x = 6, y = 7

Multiple Choice

Solve:

x = -3y - 17

2x + 3y = -7

• (1, -20)

• (10, 0)

• (-5, -2)

• (10 , -9)

Multiple Choice

What is the solution to the system of equations?

y = 3x - 8

y = 4 - x

• (3,1)

• (1,3)

• (3,-1)

• (3,-1)

Multiple Choice

x - 3y = -13
4x + 2y = 4

• (1, 4)
• (-1, -4)
• (-1, 4)
• (1, -4)

Multiple Choice

Solve:
y = -1x - 5
4x - 8y = 4

• (-3, -2)
• (5, -7)
• (3, 9)
• (-5, 4)