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MA19.8.12
Solve systems of two linear equations in two variables by graphing and substitution.

Solve systems of two linear equations in two variables by graphing and substitution.

### Unpacked Content

## UP:MA19.8.12

### Vocabulary

- System of linear equations
- Point of intersection
- One solution
- No solution
- Infinitely many solutions
- Parallel lines
- Slope-intercept form of a linear equation
- Standard form of a linear equation

### Knowledge

- The properties of operations and equality and their appropriate application.
- Graphing techniques for linear equations (using points, using slope-intercept form, using technology).
- Substitution techniques for algebraically finding the solution to a system of linear equations.

### Skills

- generate a table from an equation.
- Graph linear equations.
- Identify the ordered pair for the point of intersection.
- Explain the meaning of the point of intersection (or lack of intersection point) in context.
- Solve a system algebraically using substitution when both equations are written in slope-intercept form or one is written in standard form and the other in slope-intercept form.

### Understanding

- any point on a line when substituted into the equation of the line, makes the equation true and therefore, the intersection point of two lines must make both equations true.
- Graphs and equations of linear relationships are different representations of the same relationships, but reveal different information useful in solving problems, and allow different solution strategies leading to the same solutions.