   SEARCH HOME Math Central Quandaries & Queries  Question from Paa: a+b=8 a+c=13 b+d=8 c-d=6 find the value of each letter HI,

I am going to number the equations

1. a+b=8
2. a+c=13
3. b+d=8
4. c-d=6

Notice that the first and second equation both have an $a$ and one has a $b$ and the other a $c.$ I want to use them to get one equation with only the variables $b$ and $c.$

If I take the left side of equation 2 and subtract the left side of equation 1 then I must get the right side of equation 2 minus the right side of equation 1. That is

$(a + c)- (a + b) = 13 - 8$

which on simplification becomes

$c - b = 5.$

Equations three and four both have a $d$ and and one has a $b$ and the other a $c.$ can you do something similar to what I did with the first and second equations to obtain another equation with only the variables $b$ and $c?$

Once you have two equations in $b$ and $c$ use a similar technique to obtain an equation in only the variable $c$ solve it for $c$ and work backwards to find $a, b$ and $d.$

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.