We have learned three ways of solving systems of linear equations, namely:
a) Graphical Method
b) Substitution Method
c) Elimination Method (Addition or Subtraction)
But how do you determine which is the best method to use to make our work less tedious?
A. If equations are in slope-intercept form, the graphical method is the best method.
y = 2x + 4
y = - 1/3 x - 3
Steps: 1) Plot the y-intercept (b). This point is located on the y-axis (vertical).
2) Use the slope (rise/run) to plot a second point. You have to keep on doing this until the line crosses the x-axis.
Alternative: Find the x-intercept then plot this point on the x-axis (horizontal). Connect the two points.
3) Determine the coordinates of the point of intersection of the lines.
B. If a variable is isolated on either side of the equation, or if it is easy to isolate any variable because its coefficient is either 1 or -1, use the substitution method.
2a - b = -4
4a = 7 + 2b
Steps: 1) In either equation, solve for one variable in terms of the other.
2) Substitute for that variable in the other equation. Solve.
3) Substitute the result from Step 2 in either equation. Solve for the other variable.
4) Check the solution in both original equations.
C. Both variables are on one side and the constant is on the other side, use the elimination method.
-7c + 2d = 31
-17c - 2d = 17
Steps: 1) Add or subtract the given equations to eliminate one variable.
2) Solve the resulting equation for the remaining variable.
3) Replace the value of the known variable in any of the original equations.
4) Check the solution in both original equations.
TRY THIS!
Determine the best method to use then solve the following systems:
1) 4x + y = 6 4) 2a - b = -4
y = 2x 4a = 7 + 2b
2) -3x + y = -5 5) x - y = 3
x + 2y = 0 4x - 4y = 12
3) 2x - 3y = 7
-4x + 6y = 14