Linear Systems by Substitution

Multiple Choice

Do you have your phone in the box, notebook out, and ready to take notes? ​

(you will need to take a picture and upload it at the end)

• YES I have my notebook out

• No, I know it means a bad grade

Solving Systems by Substitution

Objective: Solve systems of equations by substitution

Math Response

Solve: 3x - 7(x - 4) = 24

Type answer here

Correct Answer: 1

Deg^°

Rad

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)

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(more of the next slide)​

​SYSTEMS OF EQUATIONS (review)

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

​EXAMPLE

​Solve the system: 2x - 3y = -1 and y = x - 1

Multiple Choice

When solving the system below, what would the second equation look like after you substitute 4x - 11 for y.

$$y=4x-11$$  and $$-4x+3y=-1$$  

• -4x + 3(4x - 11) = -1

• -4(4x - 11) + 3y = -1

• -4x + 3y = 4x - 11

Math Response

The Next Step, solve for x: $$-4x+3\left(4x-11\right)=-1$$  

Type answer here

Correct Answer: 4

Deg^°

Rad

Multiple Choice

Given what we have done so far, solve the following system:

$$y=4x-11$$ and $$-4x+3y=-1$$  

• $$\left(4,-5\right)$$  

• $$\left(-4,\ 5\right)$$  

• $$\left(4,5\right)$$  

• $$\left(5,4\right)$$  

• $$\left(-5,4\right)$$