And now ladies and gentlemen, the keeper of the keys, the countess of the clink, the mistress of murderess row:
Matron Mama Morton and Substitution!
Your Case:
Solve this system of equations:
X + 2y = 1
X + y = 2
"Got a little motto, always sees me through: When you're good to Mama, Mama's good to you!
There's a lot of favors, I'm prepared to do. You do one for Mama, she'll do one for you."
What Mama means is that in order for her to do you a favor, you must first do her a favor by making sure that one variable is by itself on one side of the equal sign.
Your case just so happens to be in the perfect form to solve with substitution because you already have a variable which is by itself. So you choose which variable you want to solve for:
X + 2y = 1
X + y = 2
Let's solve for X.
X + 2y = 1 *main problem*
-2y *subtract 2y from both sides*
X = 1-2y
Now that you know what X equals, you simply
Substitute!
Now is when you need your 2nd equation:
X + y = 2
However, instead of using X, you are going to SUBSTITUTE in your newly found X value which is 1 - 2y!
1 - 2y + y = 2
And now just solve the new equation!
1 -1y = 2 *Combine your "y" values*
-1y = 1 *Subtract 1 from both sides*
y = -1 *Divide by negative 1 on both sides*
Now that you know y = -1...........It's time for a little more Substitution!
Choose one of the two original equations:
X + 2y = 1
or
X + y = 2
We'll choose X + 2y = 1.
Subtitute in y = -1
X - 1 = 2
X = 3 *Add 1 to both sides*
Now you write your answer in point form which is
(X, y)
Your cases' defense:
(3, -1)
Congratulations you have just won your case!
"So what's the one conclusion, I could bring this number to? When you're good to Mama, Mama's good, to Yoooouuuu!"