SOLUTION: 2x + 3y = 31 y = x + 7

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: 2x + 3y = 31 y = x + 7       Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   


Question 13118: 2x + 3y = 31
y = x + 7

Answer by akmb1215(68) About Me  (Show Source):
You can put this solution on YOUR website!
You should use substitution to solve this problem. Since you know y=x+7, every time you see a y in the first equation, you can plug in x+7 in for that y. Think of it like a code that you are solving...
When you substitute that in, your top equation now looks like: 2x+%2B+3%28x+%2B+7%29+=+31.
To solve this equation, you will need to use the distributive property to distribute the 3 across the (x+7). The new equation looks like: 2x+%2B+3x+%2B+21+=+31.
Now, combine like terms to make the equation 5x+%2B+21+=+31. Move the 21 over to the other side by subtracting it from both sides of the equal sign, which gives you: 5x+=+10.
Divide by 5 on both sides to solve. x+=+2.
Now that you know x=2, you can plug x into either equation to solve for y. It is probably easier to put it into the bottom equation since that is the "easier" one.
So, y = 2 + 7. y = 9.