CCSS.Math.Content.HSA-REI.C

CCSS.Math.Content.HSA-REI.C is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSA-REI.C.5

  Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system w...

• CCSS.Math.Content.HSA-REI.C.6

  Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

• CCSS.Math.Content.HSA-REI.C.7

  Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

• CCSS.Math.Content.HSA-REI.C.8

  (+) Represent a system of linear equations as a single matrix equation in a vector variable.

• CCSS.Math.Content.HSA-REI.C.9

  (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

01

What Students Need to Do

Students find values that make every equation in a system true at the same time. They solve by graphing, substitution, or elimination. They also recognize when a system has no solution or infinitely many solutions.

02

What Mastery Looks Like

Students select graphing, substitution, or elimination and carry out the method accurately. They verify solutions and identify systems with one solution, no solution, or infinitely many solutions.

03

Common Misconceptions

Students may find where only one equation is true instead of checking both. Sign errors often appear during elimination or substitution. Students may also confuse parallel lines with infinitely many solutions.

04

How to Assess It

Give the system y = 2x + 1 and y = -x + 7. Ask students to solve it, name their method, and verify the ordered pair in both equations.

1. 01

   Overlay two equations drawn on transparent coordinate grids, then mark the intersection and check its coordinates in both equations.

2. 02

   Ask students to explain which method they would choose for three different systems and defend each choice in writing.

3. 03

   Play a matching game connecting system cards with solution cards, graph cards, and labels for one, none, or infinitely many solutions.

4. 04

   Model ticket prices with two equations, then solve to find the number of adult and student tickets sold.

• CCSS.Math.Content.HSA-REI.B

  Solve equations and inequalities in one variable

• CCSS.Math.Content.8.EE.C.7

  Solve linear equations in one variable.

• CCSS.Math.Content.8.EE.C.8

  Analyze and solve pairs of simultaneous linear equations.

• CCSS.Math.Content.8.EE.C.8b

  Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.