Solving Word Problems Using Systems Of Equations

Solving Word Problems Using Systems Of Equations-50
Then we add the two equations to get “\(0j\)” and eliminate the “\(j\)” variable (thus, the name “linear elimination”). Now that we get \(d=2\), we can plug in that value in the either original equation (use the easiest! We then get the second set of equations to add, and the \(y\)’s are eliminated. Now we can plug in that value in either original equation (use the easiest! Sometimes, however, there are no solutions (when lines are parallel) or an infinite number of solutions (when the two lines are actually the same line, and one is just a “multiple” of the other) to a set of equations.When there is at least one solution, the equations are consistent equations, since they have a solution.

In this type of problem, you would also have/need something like this: .

Now, since we have the same number of equations as variables, we can potentially get one solution for the system.

So the points of intersections satisfy both equations simultaneously.

We’ll need to put these equations into the \(y=mx b\) (\(d=mj b\)) format, by solving for the \(d\) (which is like the \(y\)): First of all, to graph, we had to either solve for the “\(y\)” value (“\(d\)” in our case) like we did above, or use the cover-up, or intercept method.

So, again, now we have three equations and three unknowns (variables).

Ed Biology A2 Coursework Specification - Solving Word Problems Using Systems Of Equations

We’ll learn later how to put these in our calculator to easily solve using matrices (see the Matrices and Solving Systems with Matrices section), but for now we need to first use two of the equations to eliminate one of the variables, and then use two other equations to eliminate the same variable: Now this gets more difficult to solve, but remember that in “real life”, there are computers to do all this work!The easiest way for the second equation would be the intercept method; when we put for the “\(d\)” intercept.We can do this for the first equation too, or just solve for “\(d\)”.Now let’s see why we can add, subtract, or multiply both sides of equations by the same numbers – let’s use real numbers as shown below.Remember these are because of the Additive Property of Equality, Subtraction Property of Equality, Multiplicative Property of Equality, and Division Property of Equality: \(\displaystyle \begin\color\\\,\left( \right)\left( \right)=\left( \right)6\text\\,\,\,\,-25j-25d\,=-150\,\\,\,\,\,\,\underline\text\\,\,\,0j 25d=\,50\\25d\,=\,50\d=2\\d j\,\,=\,\,6\\,2 j=6\j=4\end\). \(\displaystyle \begin\color\,\,\,\,\,\,\,\text-3\\color\text\,\,\,\,\,\,\,\text5\end\) \(\displaystyle \begin-6x-15y=3\,\\,\underline\text\\,29x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=58\\,\,\,\,\,\,\,\,\,\,\,\,\,x=2\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\2(2) 5y=-1\\,\,\,\,\,\,4 5y=-1\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5y=-5\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y=-1\end\) ). In the example above, we found one unique solution to the set of equations.This means that the numbers that work for both equations is 4 pairs of jeans and 2 dresses! Here is the problem again: Solve for \(d\): \(\displaystyle d=-j 6\).We can also use our graphing calculator to solve the systems of equations: Solve for \(y\,\left( d \right)\) in both equations. Plug this in for \(d\) in the second equation and solve for \(j\). Note that we could have also solved for “\(j\)” first; it really doesn’t matter.It’s easier to put in \(j\) and \(d\) so we can remember what they stand for when we get the answers.There are several ways to solve systems; we’ll talk about graphing first.It’s much better to learn the algebra way, because even though this problem is fairly simple to solve, the algebra way will let you solve any algebra problem – even the really complicated ones.The first trick in problems like this is to figure out what we want to know.


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