Deciding when to use the substitution method
Consider this system of 2 equations 2x + y = 11 x + 3y = 13
NOTICE the y in the first equation has a coefficient of 1. The x in the second equation also has a coefficient of 1
When you have a coefficient of 1 for any variable, substitution is a good method to choose
Let's use the substitution method to solve our system: 2x + y = 11 x + 3y = 13
First we will take the second equation and isolate x because it has it has a coeffiecient of 1 (the 1 is invisible!)
When we solve x + 3y = 13 for x
we get x = -3y + 13
This means we can REPLACE x with -3y + 13 in our other equation!
Recall: our system is 2x + y = 11 x + 3y = 13
We will now SUBSTITUTE -3y + 13 for x in the first equation:
2(-3y + 13) + y = 11
Now we have 1 equation with 1 variable and we can solve it!
2(-3y+13) + y =11
-6y + 26 + y = 11
-5y + 26 = 11
-5y = -15
y = 3
Now that we know what the value of y is we can figure out x!
2x + y = 11 x + 3y = 13
Since we used the top equation to find y, we will use the bottom equation to find x
Substitute 3 in for y in the bottom equation to get:
x + 3(3) = 13
now solve for x!
x + 9 = 13 x = 4
The solution to our system is the point (4, 3)