Learn about Linear Equations Solution Applications In this lesson, let’s learn how we solve linear equations. We’ll try two different problems. The first problem says that to find a baseball pitcher’s earned run average or ERA we can use the formula Ei=9r where E represents the ERA, small letter i represents the number of innings pitched and r represents the number of earned runs allowed. We need to solve the equation for E. So let’s write the formula down. The formula is Ei=9r. Now anytime we look at our formula, our formula describes the relationship between the different quantities so as we can see in this formula here Ei=9r. So if we want to solve the equation for E we need to use inverse operations. As we can see E is multiplied by i to get 9r. So if I divide both sides by i, what do I get? I will get Ei/i is E=9r/i. So if we want to solve for E the way we do that is we multiply 9r/i and that will give us the value for E. So let’s do that. When we are given, if he allows 8 runs in a 24 innings pitch. So this i in 8 runs so this is r. So we’re given the value of r and i, so what do we compute? If we want to look at E = 9(8) and we need to divide by the number of innings pitch which is 24. So 9 x 8 = 72 divided by 24 gives us 3. So in this case, the ERA or earned run average equals 3. All we did was we looked at the formula which was Ei=9r and solve it for the variable E big on the left everything else big on the right. We did that by inversing the operations since E was multiplied by we divide it by i to get E on one side all by itself. And since we got the new formula we can apply the values to the new formula to get the answer. Let’s try one other problem. In this case we are given m/n=p-8. We need to solve this for n so what I need to do is bring n to one side by itself. So if m/n=p-8 that means n/m if I reverse, if I flip and round this gets 1/p-8. All I did was flipped the numerator and denominator or add. Since I want n on one side I can multiply it by m here, I can multiply by m here, what does that give me, m and m cancels out so n=m/p-8. That is the formula for n on one side equals m/p-8. That’s the formula or that’s how we solve for this equation or solve for n.