step 1: Decide to cancel either a or b
For a: The coefficients 3 and 3 cancel perfectly through subtraction
For b: The coefficients 5 and 1 do not cancel easily.
We will choose to cancel a using subtraction
We will subtract because we want to cancel 3a with 3a
Using the equation from step 2, we will isolate b
Using the value of a from step 3, we can solve for b using either of the original equations
We do this by substituting a with its value.
step 1: Decide how to cancel either x or y
For x: the coefficients of 5 and -5 can cancel perfectly through addition
For y: the coefficients of 3 and -5 do not cancel easily
we will choose to cancel the x terms through addition
We will do an addition because we want to cancel -5x with 5x
Using the equation from step 2, we will isolate y
Using the value of y we found in step 3, we can solve for x using either of the original equations
We do this by replacing y with its value
step 1: Adjusting the equations
For f: the coefficients of 2 and 3 do not easily cancel
For g: the coefficients of 4 and -5 do not cancel easily through addition or subtraction.
We can choose to adjust the equations so we can adjust either the f terms or the g terms. In this example, we will cancel the f terms.
We multiply both sides of the first equation by 3
Now we will multiply both sides of the second equation by 2
Now our adjusted equations have coefficients for the f terms of 6f and 6f which can be cancelled through subtraction
From here we can solve for g
step 4: Using the value of g from step 3 we can solve for f