Hi, there--
THE PROBLEM:
Solve the simultaneous equations:
x - y = 3
3y - 3x = 4
A SOLUTION:
Let's use the elimination method to solve this system of equations. Change the order of the x- and
y-terms in the second equation so that both equation have x and y in the same order. I change the
subtraction to an addition because addition is commutative and subtraction is not.
3y - 3x = 4
3y + (-3x) = 4
-3x + 3y = 4
We want to add the equations together and eliminate one variable (In this case, the x-term.) Notice that
the coefficient of the x-term in the second equation is -3. We need to multiply both sides of the first
equation by the additive inverse of -3. That is 3.
x - y = 3 -----> 3x - 3y = 12
Now the x-terms will cancel out when we add the equations together.
3x - 3y = 12
-3x + 3y = 4
-------------
0 + 0 = 16
0 = 16
When we see a situation like this, where both variables disappear, it means that the system of equations has no solution.
Let's look at the graph to see what's happening:
The green equation is x - y = 3. The red one is 3y - 3x = 4.
The solution to a system of simultaneous equations is the point or points they have in common. We see
that these lines are parallel, so they will never intersect. Thus there is no solution to this system. The
official math terminology is that this system is inconsistent.
Hope this helps! Feel free to email if you have any questions about the solution.
Good luck with your math,
Mrs. F
math.in.the.vortex@gmail.com
