Consider: a + b = 5 2 a + b + c = 4 a − b − c = 5I like to use substituiton for solving systems of equations, so I firstly look at equation 1 and solve for a a + b = 5 a = 5 − bI substitute this into equation 2 2 ( 5 − b ) + b + c = 4 10 − 2 b + b + c = 4 − b = 4 − c − 10 b = − 4 + c + 10What next? Am I on the right track? Can I use substitution method for any simultaneous equation?

Question

Consider:  a  +  b  =  5   2  a  +  b  +  c  =  4  a  −  b  −  c  =  5I like to use substituiton for solving systems of equations, so I firstly look at equation 1 and solve for   a  a  +  b  =  5  a  =  5  −  bI substitute this into equation 2  2  (  5  −  b  )  +  b  +  c  =  4  10  −  2  b  +  b  +  c  =  4  −  b  =  4  −  c  −  10  b  =  −  4  +  c  +  10What next? Am I on the right track? Can I use substitution method for any simultaneous equation?

Sawyer Day · Accepted Answer

You have the right concept, and we can see from three equations and three unknowns that these variables are solvable (taking into account equations are linearly independent)equation 1:      a  +  b  =  5equation 2:      2  a  +  b  +  c  =  4equation 3:      a  −  b  −  c  =  5lets solve for   b first:from equation 1 and 3, we say  a  =  5  −  b and      c  =  a  −  b  −  5Now we plug these two &#039;new&#039; equations into equation 2:     2  (  5  −  b  )  +  b  +  (  (  5  −  b  )  −  b  −  5  )  =  4simplifying for   b gives that   b  =  2.Now taking that   b  =  2, we can sub that back into equation 1 and solve for a and once we have a we can use   a and   b to solve for   c. Which I&#039;m sure you&#039;ll be able to solve for it.

Arraryeldergox2 · Accepted Answer

Substitution is not the best way to go about this kind of problem. Use reduction instead. For example if we add the second and third equations together we get  3  a  =  9so we know that   a  =  3 immediately. The first then gives us that   b  =  2 and finally   c  =  −  4. Much easier and hardly any work.

Consider: a + b = 5 2 a + b + c = 4 a &#x221

Answered question

Answer & Explanation

New Questions in Algebra I