# Solving Word Problems Using Systems Of Equations 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.

## Comments Solving Word Problems Using Systems Of Equations

• ###### Solving Systems of Equations Word Problems - Algebra Class
Reply

First we started with Graphing Systems of Equations. Then we moved onto solving systems using the Substitution Method. In our last lesson we used the Linear.…

• ###### Systems of Equations Word Problems -.
Reply

Nov 7, 2007. For a complete lesson on systems of equations word problems, go to. to solve number and value word problems using a system of linear.…

• ###### System-of-Equations Word Problems Purplemath
Reply

Demonstrates typical "system of equations" word problems, including "mixture". Many problems lend themselves to being solved with systems of linear equations. In "real. Using a system of equations, however, allows me to use two different.…

• ###### Systems of Equations Word Problems - Kuta Software
Reply

Systems of Equations Word Problems. 1 Find the value of two numbers if their sum is 12 and their difference is 4. 2 The difference of two numbers is 3.…

• ###### Mixture problems systems of equations in two variables
Reply

The first of our equations will come from the amount of liquid in the bottles-- adding the liquid together in the two bottles will give us 20 ounces of solution.…

• ###### Solve a system of equations using any method word problems
Reply

Improve your math knowledge with free questions in "Solve a system of equations using any method word problems" and thousands of other math skills.…

• ###### System of equations word problem walk & ride video Khan.
Reply

Systems of equations can be used to solve many real-world problems. In this video, we solve a problem about distances walking and riding bus to school.…

• ###### Solve a system of equations using elimination word problems
Reply

Improve your math knowledge with free questions in "Solve a system of equations using elimination word problems" and thousands of other math skills.…

• ###### Systems of Linear Equations and Word Problems – She Loves.
Reply

Probably the most useful way to solve systems is using linear combination, or linear.…

• ###### Systems of equations with elimination apples and oranges.
Reply

System of equations word problem no solution. Now you have a system of three equations and three variables and you can solve using your algebra skills.…