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|Solve systems of linear equations, in two
The intersection of the graph of two linear equations is the point(s) of intersection between the two lines.
NOTE: The fastest and easiest method of graphing is using the slope-intercept method (y=mx+b).
There are 3 types of solutions to systems of linear relations:
Note: If there are no solutions, the system is inconsistent. If there is at leason one solutions, the system is either independent or dependent.
Linear Systems Interactive Activity
Focus attention on the y = mx + b form for LINE ONE and LINE TWO.
Process for a system of 2 linear equations using the variables c and d:
Process for a system of 2 linear equations using the variables x and y:
Sample solution: In this case the system of 2 equations can be added to eliminate y.
Process for a system of 2 linear equations using two variables:
- Pick a variable to eliminate. Take a close look as one choice will likely make the solution simpler.
- Decide what the common multiple is for the coefficients of the two variables.
- For 4x and 8x, the common multiple will be 8x.
- For 2a and 3a, the common multiple will be 6a.
- Determine the factor needed to multiply by to make a new equation that will have the common multiple for the variable selected.
- Create new equation(s) my multiplying by the factor(s) determined.
- Add or subtract the new system of equations to eliminate one of the variables.
- Isolate the remaining variable in the sum.
- Use the isolated value to determine the value of the second variable.
- Check your work.
- Report the answer as an ordered pair (x, y)
Sample solution 1 (One Step) In this case multiply the first equation by 2. Subtract second equation from this new equation this new equation to eliminate x.
Sample solution 2 (Two Step) In this case multiply the first equation by 2 and the second equation by 3. Subtract the fourth equation from the third equation to eliminate a.
Parts of this work has been adapted from a Math 20 Pure learning resource originally produced and owned by Alberta Education.