You can solve for two variables only if you have two distinct equations. Two forms of the same
equation will not be adequate. Combine the equations in such a way that one of the variables
cancels out. For example, to solve the two equations 4 x + 3y = 8 and x + y = 3, multiply both sides of
the second equation by −3 to get −3x − 3y = −9. Now add the two equations; the 3y and the −3y
cancel out, leaving x = −1. Plug that back into either one of the original equations, and you’ll find
that y = 4.
Example 9 is a simultaneous equations question.
Example 9If you just plow ahead without thinking, you might try to answer this question by solving for one
variable at a time. That would work, but it would take a lot more time than this question needs. As
usual, the key to this simultaneous equations question is to combine the equations, but combining
the equations doesn’t necessarily mean losing a variable. Look what happens here if you just
subtract the equations as presented:
Suddenly, you’re almost there. Just divide both sides by 2, and you get . The
answer is (B).
1. If 3s + 5t = 10 and 2s − t = 7, what is the value of ?