Use a system of equations

Can you explain to me how to solve the following problem?

Isaac bought school shirts for $35 each and school pants for $49 each. If he buys 9 items and his total cost is $357, how many shirts did he buy?

I solved it with trial and error, but I know there is an algebraic method. 

Thank you.

---

Make a system of two equations.  Let the variables represent what you do not know, the number of shirts and
the number of pants.

x = number of shirts
y = number of pants

x + y = 9  {he buys 9 items}
35x + 49y = 357  {shirts are $35 each, pants are $49 each, the total is 357}

Use the elimination method to solve the system, multiplying the top equation by -35, and then adding 
the two equations together.  This will eliminate the x.  You could also multiply the top equation by
-49 and add together, or even use the substitution method.

-35x - 35y = -315   {multiplied first equation by -35}
35x + 49y = 357   {second equation stays the same}
----------------
14y = 42   {added the two equations together}
y = 3  {divided each side by 14}

x + y = 9   {first original equation}
x + 3 = 9  {substituted 3, in for y, into first equation}
x = 6   {subtracted 3 from each side}

He bought 6 shirts and 3 pants

Ask Algebra House