This week, we covered systems of linear equations. Systems give us two lines, and we are supposed to find the point at which these two lines intersect. We learned about three different methods to solve systems. One of these ways was to simply graph the two lines given and see where they intersect.
Another solution is to substitute one equation for another. Say you have two equations:
- 3x+2y=4
- x-3y=5
x is currently by itself. Simply isolate x, and the equation is now x=3y+5
Substitute x into the first equation, and you now have 3(3y+5)+2y=4. Expanded, it is 11y=-11. We now know y=-1
Substitute y=-1 into one of the equations, x-3(-1)=4
x+3=4. This means x=1
The lines intersect at (1,-1)