# Solving Systems By Substitution Word Problems

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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.

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!

This means that the numbers that work for both equations is We can see the two graphs intercept at the point $$(4,2)$$. It involves exactly what it says: substituting one variable in another equation so that you only have one variable in that equation.

This will help us decide what variables (unknowns) to use.

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 “$$d$$”).

When equations have no solutions, they are called inconsistent equations, since we can never get a solution.

Here are graphs of inconsistent and dependent equations that were created on the graphing calculator: Let’s get a little more complicated with systems; in real life, we rarely just have two unknowns with two 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.