Systems of Linear Equations
The word problems we looked at in the previous section were obvious. They practically shouted out, "Look! I'm a word problem and I'm talking about two lines!'' Aside from their outbursts being needlessly loud and distracting us from our cross-stitching, it's also a little presumptuous of them to assume we care. Now we're going to get more subtle, not to mention quieter. These problems are more likely to whisper than shout, which is good news for our ears as well as this monogrammed pillowcase we're working on.
When we solve a system of two linear equations, we're using two pieces of information (the two equations) to find two unknown quantities (usually called x and y).
When a word problem contains two quantities we don't know and gives us two pieces of information about these quantities, we can write a system of equations to describe the word problem. Then we can use that system of equations to solve the problem.
There are three main parts to solving one of these word problems.
- Describe the word problem using a system of equations.
- Solve the system of equations.
- Check your answers.
The first part tends to be the most troublesome, so we're going to worry about it first. We also like to deliver bad news before delivering good news, so if we ever tell you we've got some good news and some bad news, brace yourself.