Please enable JavaScript.
Coggle requires JavaScript to display documents.
System of Equations of 2 Variables, What methods can we use to solve the…
System of Equations of 2 Variables
What is a system of equations?
System of equations are two or more equations to be solved together.For a system to have a unique solution, the number of equations must equal the number of unknowns.A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
What does it look like?
A system of linear equations is usually a set of two linear equations with two variables. x + y = 5 x+y=5 x+y=5x, plus, y, equals, 5 and 2 x − y = 1 2x-y=1 2x−y=12, x, minus, y, equals, 1 are both linear equations with two variables.
Examples
Real Life
Systems of equations can be used when trying to determine if you'll make more money at one job or another, taking multiple variables into account, such as salary, benefits and commissions.
There are 3 ways to solve systems of linear equations in two variables:Graphing,Substitution Method and Elimination Method.
What methods can we use to solve the System of Equations?
Elimination Method
Write both equations in standard form. ...
Make the coefficients of one variable opposites. ...
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
Substitution Mehtod
Solve one of the equations for either variable.
Substitute the expression from Step 1 into the other equation.
Solve the resulting equation.
Substitute the solution in Step 3 into one of the original equations to find the other variable.
Write the solution as an ordered pair.
Graphing Method
Graph the first equation.
Graph the second equation on the same rectangular coordinate system.
Determine whether the lines intersect, are parallel, or are the same line.
Identify the solution to the system. If the lines intersect, identify the point of intersection.
1.
2.
3.
4.
5.
1.
2.
3.
4.
1.
2.
3.
4.
5.
