DDTDataDrivenTalesMath 1 Summer Bridge

Math 1 Summer Bridge

Day 6: Systems of Equations

Understand systems as two relationships and find the solution where they agree.

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Student Goal

I can solve a simple system by graphing, substitution, or elimination reasoning.

Why It Matters

Systems help compare two choices, two plans, or two patterns. They are a major Math 1 topic.

Warm-Up

Warm-Up 1

What does the intersection point of two lines represent?

Warm-Up 2

Does (2,5) satisfy y = 2x + 1?

Short Lesson

Standard Focus

NC.M1.A-REI.5 and NC.M1.A-REI.6: Systems of linear equations

Student-Friendly Standard Goal

I can explain the solution to a system as the point where two equations have the same values.

  • A system is a set of two or more equations considered together.
  • The solution is an ordered pair that makes both equations true.
  • On a graph, the solution is the intersection point.
  • Substitution works well when one equation already has y = or x =.

Guided Examples

Guided Example 1

Solve by Substitution

Solve the system y = x + 4 and y = 2x + 1.

Step 1

x + 4 = 2x + 1

What is x?

Guided Example 2

Interpret a System

Plan A costs 10 plus 2 per visit. Plan B costs $4 per visit. When are they equal?

Step 1

2v + 10 = 4v

What is v?

Practice

Problem 1

Which point solves y = x + 2 and y = 5?

Problem 2

Solve for x: x + 6 = 3x.

Problem 3

If two lines never intersect, the system has...

Problem 4

Choose the next step: y = 3x - 1 and y = x + 5.

Problem 5

True or false: A system solution should make both equations true.

Reflection

How are you feeling about today's skill?

Optional reflection: What is one step, word, or representation from today that you want to remember when Math 1 starts?