This was our last week before our Graphing Inequalities and Systems test. We were learning right up until the day before so there has still been a lot to cover.
One cool topic from this week was solving systems algebraically. Let me explain.
I really liked this part of the unit because you are letting the math do the work for you.
Take the system
and
We can use a method called “substitution” to fill in a variable with another one. This means all we have to do is isolate one variable and then replace it in the other equation. Lucky for us, y is already isolated so all we have to do is plug and play in the other equation.
Now we have
From here we can go to
We have to make it equal 0, so we bring the 360 into the equation. Since they cancel out, we are no left with
From here we can factor to
Now we have to solve and make this true. To do this, we need to figure out the x values to make it 0.
Obviously, the first one would be 0 since multiplying the entire equation by 0 makes it 0.
The second one would be 30 since we need to end up with 0.
Now that we have our x-values, we can go back and plug them into the original equation to solve for y.
y = -12
AND
y =18
Now with our y-values, we have our solutions which are (30,18) and (0,-12)
Nice and easy!