A.2.13.2 Four Systems
We are now going to solve the four systems of equations you saw earlier.
We are going to use a method called substitution - this means just what it sounds like.
You will be substituting one equation into the other equation.
Let's do the first one together.
Below is our system, we are going to substitute the 2nd equation into the 1st equation.
The 2nd equation tells us that x = -5, so were going to substitute -5 for x in the 1st equation.
x + 2y = 8 becomes:
-5 + 2y = 8 now this is an equation we can solve.
+5 +5
2y = 13
y = 6.5
So the point where these lines would cross on a graph is (-5, 6.5) or another way to say that would be that when x = -5 and y = 6.5 these equations are both true. Let's check that!
x + 2y = 8, plug in x = -5 and y = 6.5 to see if makes 8
-5 +2(6.5)
-5 + 13
8 yep, x = -5 and y = 6.5 makes the first equation true!
There isn't much to check with the 2nd equation:
x = -5 yep, x = -5 and y = 6.5 makes the second equation true!
The 2nd equation tells us that x = -5, so were going to substitute -5 for x in the 1st equation.
x + 2y = 8 becomes:
-5 + 2y = 8 now this is an equation we can solve.
+5 +5
2y = 13
y = 6.5
So the point where these lines would cross on a graph is (-5, 6.5) or another way to say that would be that when x = -5 and y = 6.5 these equations are both true. Let's check that!
x + 2y = 8, plug in x = -5 and y = 6.5 to see if makes 8
-5 +2(6.5)
-5 + 13
8 yep, x = -5 and y = 6.5 makes the first equation true!
There isn't much to check with the 2nd equation:
x = -5 yep, x = -5 and y = 6.5 makes the second equation true!Now it's your turn to try:
Solve the system below using substitution (be sure to check your answer):
This one is a little trickier (but I know you can do it!):
Solve the system below using substitution (be sure to check your answer):
This one is even more tricky (but I know you can do it too!):
Solve the system below using substitution (be sure to check your answer):
