Wonderlic Mathematics Review: Systems of Equations

Systems of Equations are a set of simultaneous equations that all use the same variables. A solution to a system of equations must be true for each equation in the system. Consistent Systems are those with at least one solution. Inconsistent Systems are systems of equations that have no solution.
To solve a system of linear equations by substitution, start with the easier equation and solve for one of the variables.
Express this variable in terms of the other variable.
Substitute this expression in the other equation, and solve for the other variable.
The solution should be expressed in the form (x, y).
Substitute the values into both of the original equations to check your answer.

Consider the following problem:  Solve the system using substitution:



Solve the first equation for x:


Substitute this value in place of x in the second equation, and solve for y:





Plug this value for y back into the first equation to solve for x:


Check both equations if you have time:


Therefore, the solution is (9.6, 0.9).

To solve a system of equations using elimination, begin by rewriting both equations in standard form .
Check to see if the coefficients of one pair of like variables add to zero.
If not, multiply one or both of the equations by a non-zero number to make one set of like variables add to zero.
Add the two equations to solve for one of the variables.
Substitute this value into one of the original equations to solve for the other variable.
Check your work by substituting into the other equation.
Next we will solve the same problem as above, but using the addition method.

Solve the system using elimination:



If we multiply the first equation by 2, we can eliminate the y terms:



Add the equations together and solve for x:



Plug the value for x back into either of the original equations and solve for y:



Check both equations if you have time:


Therefore, the solution is (9.6, 0.9).