5/19 Alg1: Introduction to Solving by Substitution

Solving Systems of Equations by Substitution

Our 2nd of 3 methods of solving!

Recall: Solution by Graphing

• Graph the system of equations

• Identify the point of intersection: this is the solution to the system!

Learning Target

I can solve a system of equations by substitution.

Open Ended

I'm thinking of two numbers that add to 4. One of the numbers is 3.

What is the other number?

Multiple Choice

Solve for y:

$$x+y=4$$   $$x=3$$  

• $$y=1$$  

• $$y=-1$$  

• $$y=3$$  

• $$y=0$$  

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This is a system of equations!

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x+y = 4 x = 3

Take a look at the graph of the system. What do you notice about the solution?

Multiple Choice

Solve for x: 

$$x+y=4$$   $$y=3$$  

• $$x=0$$  

• $$x=-1$$  

• $$x=1$$  

• $$x=3$$  

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Solve the system of equations:

y = -x + 4 y = 3

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The answer should be an (x, y) point that exists on both lines. 

We know y has to equal 3, and we found that x has to equal 1.  SOLUTION: (1, 3)

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Multiple Choice

Solve the system of equations:

$$x+y=4$$   $$y=2$$  

• $$\left(2,\ 0\right)$$  

• $$\left(2,\ 4\right)$$  

• $$\left(1,\ 1\right)$$  

• $$\left(2,\ 2\right)$$  

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Solve the system of equations:

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 x + y = 4

 y = x + 2

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What can we do now?

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Multiple Choice

Solve the system of equations by substitution:

$$x+y=10$$   $$y=x+4$$  

• $$\left(5,\ 5\right)$$  

• $$\left(3,\ 7\right)$$  

• $$\left(1,\ 9\right)$$  

• $$\left(1,\ 5\right)$$  

What does this look like in life? Consider the following scenario.

A basketball team scored 45 points through a combination of both 2-pointers and 3-pointers.

If they made the same number of 2-point shots as 3-point shots, how many 2-point shots did they make?

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How many 3-point shots did they make?

Let's create a system of equations!

• A basketball team scored 45 points through a combination of both 2-pointers and 3-pointers.

• They made the same number of 2-point shots as they did 3-point shots.

• Equation 1:

• Equation 2:

Solve the systems of equations by Substitution

• A basketball team scored 45 points through a combination of both 2-pointers and 3-pointers.

• They made the same number of 2-point shots as they did 3-point shots.

• Solve for x and y.

Solution

Debrief

Learning Target: I can solve a system of equations by substitution.

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There are 3 methods of solving systems of equations: we know of graphing and substitution.

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To solve by substitution, solve one of the equations to be set equal to one variable (y or x) and substitute into the other equation. Solve for both variables.

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Great work today! COMPLETE YOUR EXIT TICKET.