# Solving Linear Systems of Equations

12 apples & 8 guavas total cost is Rs. 76/-. 8 apples & 12 guavas cost is Rs. 64/-. What is the cost of each apple & guava?

### Comments for Solving Linear Systems of Equations

Average Rating     Nov 18, 2010 Rating     Solving Linear Systems of Equations by: Karin I'm not sure what you mean by: Rs. 76/- I'm thinking that this is the form of currency that you use in your country. If 12 apples and 8 guavas cost RS. 76, then we could write this equation as: Let a = apples Let g = guavas 12a + 8g = 76 If 8 apples and 12 guavas cost RS. 64, then we could write this equation as: 8a + 12g = 64 Now that you have written two equations, you have written a system of equations. With this system you can choose one of three methods to solve: substitution, linear combinations, or graphing. Since the equations are written in standard form, I find the easiest method to use is linear combinations. Step 1: We must create one set of opposite terms. I am going to create opposite "g" terms by multiplying the first equation by -3 and the second equation by 2. -3[12a + 8g] = -3 -36a - 24g = -228 Now the second equation we must multiply by 2: 2[8a +12g] = 64 16a + 24g = 128 Now our two new equations are: -36a - 24g = -228 16a + 24g = 128 Notice that we have opposite terms (-24g & 24g) Step 2: Add the two equations: -36a - 24g = -228 16a + 24g = 128 --------------------- -20a + 0 = -100 Step 3: Solve for a -20a/-20 = -100/-20 a = 5 So now we know that we have 5 apples. Step 4: Substitute 5 for a and solve for g in one of the equations. 8a + 12g = 64 8(5) + 12g = 64 40 + 12g = 64 40 -40 +12g = 64 - 40 12g = 24 12g/12 = 24/12 g = 2 So, now we know that we have 2 guavas. The solution is 5 apples and 2 guavas. You can substitute these numbers into the original equations to check. Hope this helps! Karin