Lesson on Solving Systems

Solving Systems (part 1)

Objective: Solve systems of equations using substitution.

What is a System of Equations?

It is simply two or more equations.

On the graph is ...

y = 2x + 1

y = -x + 7

To solve a system, you find the point where the lines intersect.

On this graph it is (2,5)

The SOLUTION (2,5) makes each equation true.

Plug in to each equation.

y = 2x + 1

5 = 2(2) + 1

5 = 4 + 1

5 = 5

y = -x + 7

5 = -2 + 7

5 = 5

Multiple Choice

What is the solution to this system of equations?

• (-1,4)

• (4,1)

• (4,-1)

• (1,4)

We will only work with two equations

​There is more than one way to solve systems.

The one I just showed was graphically.

We are not going to focus on that method.

I used it as an example so you would understand what the answer was

(as in where the lines cross)

​

We are going to focus on the method of SUBSTITUTION

​

​So let's look at a couple of different situations where we can use substitution.

Example 1

y = 4x - 1

​y = 2x - 5

Multiple Choice

Solve the following system:

$$y=-x-1$$  

$$y=-5x-17$$  

• $$\left(-4,3\right)$$  

• $$\left(4,\ 3\right)$$  

• $$\left(3,\ 4\right)$$  

• $$\left(3,\ -4\right)$$  

Example 2

y = 3x + 8

​5x + 2y = 5

Multiple Choice

Solve the following system:

$$y=4x-11$$  

$$-4x+3y=-1$$  

• $$\left(4,-5\right)$$  

• $$\left(-4,\ 5\right)$$  

• $$\left(4,5\right)$$  

• $$\left(5,4\right)$$  

• $$\left(-5,4\right)$$  

Example 3

3x + 5y = 13

​2x + y = 4

Multiple Choice

Solve the following system:

$$6x+y=6$$  

$$-3x+2y=-18$$  

• $$(-6,2)$$  

• $$(6,-2)$$  

• $$(2,-6)$$  

• $$(-6,-2)$$  

• $$\left(-2,-6\right)$$