Solving Problems With Linear Systems

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.

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We can do this for the first equation too, or just solve for “\(d\)”.

We can see the two graphs intercept at the point \((4,2)\). Push ENTER one more time, and you will get the point of intersection on the bottom! Substitution is the favorite way to solve for many students!

The third method for solving a system of linear equations is to graph them in the plane and observe where they intersect.

We'll go back to our same example to illustrate this.

What we want to know is how many pairs of jeans we want to buy (let’s say “\(j\)”) and how many dresses we want to buy (let’s say “\(d\)”).

Always write down what your variables will be: equations as shown below.Now, you can always do “guess and check” to see what would work, but you might as well use algebra!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.Convenient systems usually seem very tough to solve at first.Often times a clever insight will make things much easier.Notice that the \(j\) variable is just like the \(x\) variable and the \(d\) variable is just like the \(y\).It’s easier to put in \(j\) and \(d\) so we can remember what they stand for when we get the answers.Solve the following system: So then subtracting the first equation from this leaves on the LHS and on the RHS.Subtracting this equation from the second equation leaves on the LHS and on the RHS.“Systems of equations” just means that we are dealing with more than one equation and variable.So far, we’ve basically just played around with the equation for a line, which is \(y=mx b\).

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