
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 1st, 2015, 09:01 AM  #1 
Member Joined: Aug 2014 From: Lithuania Posts: 60 Thanks: 3  System of equations
I need to solve for a and b: $\displaystyle 10a+b7=3a+3b$ $\displaystyle a^2+b^2ab=10a+b$ I can't find a way how to do it. Please help! 
March 1st, 2015, 09:17 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361 
From the first equation, can you write b in terms of a?

March 1st, 2015, 09:21 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,193 Thanks: 504 Math Focus: Calculus/ODEs 
I would begin by simplifying the first equation by combining like terms so that we have the system: $\displaystyle 7a2b=7\tag{1}$ $\displaystyle a^2+b^2ab=10a+b\tag{2}$ Now, solve (1) for $a$, and then substitute into (2)...you will get a quadratic in $b$... 
March 1st, 2015, 02:27 PM  #4 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
$\displaystyle 10a+b7=3a+3b$ $\displaystyle b3b=3a10a+7$ $\displaystyle 2b=7a+7$ $\displaystyle 2b=7a7$ $\displaystyle b=\frac{7a7}{2}$ $\displaystyle a^2+(\frac{7a7}{2})^2a(\frac{7a7}{2})=10a+(\frac{7a7}{2})$ $\displaystyle a^2+(\frac{49a^298a+49}{4})(\frac{7a^27a}{2})=10a+(\frac{7a7}{2})$ $\displaystyle 4a^2+49a^298a+4914a^2+14a=40a+14a14$ $\displaystyle 39a^2138a+63=0$ $\displaystyle 13a^246a+21=0$ $\displaystyle (13a7)(a3)=0$ $\displaystyle a=3, a=\frac{7}{13}$ $\displaystyle b=\frac{7(3)7}{2}=7$ $\displaystyle b=\frac{7(\frac{7}{13})7}{2}=\frac{21}{13}$ $\displaystyle \therefore a=3,b=7 ; a=\frac{7}{13},b=\frac{21}{13}$ 

Tags 
equations, sustem, system 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The system of equations (64 equations 12 unknown) solution  ZeusTheMunja  Linear Algebra  20  January 25th, 2013 05:52 AM 
System of equations  zana93  Algebra  1  July 12th, 2012 10:02 AM 
system of equations on NT  Pell's fish  Number Theory  1  March 26th, 2012 05:18 AM 
System of equations  proglote  Algebra  8  July 31st, 2011 04:22 AM 
System of Equations  aviation officer  Algebra  4  March 8th, 2011 10:08 AM 