# System of LINEAR equations: Two Equations containi

# System of LINEAR Equations : Two Equations

**Recall:** A system of equations is a collection of equations with common
variables.

**Recall:** The solutions to a system of equations are the sets of values
for the variables which make

every equation true .

If a system of equations has two variables , the solutions can be stated as
ordered pairs.

If a system of equations has three variables, the solutions can be stated as
ordered triples .

**Recall:** Linear equations of two variables are equations whose graph
can be represented by a line.

The equation can be represented where every variable has an exponent of either 1
or 0.

Nonlinear equations of two variables are equations that aren’ t linear .

**Recall: **There are four methods to solving systems of linear equations:
finding intersection points of

the graph, the method of substitution , the method of elimination, and
applications of matrices.

** Solving Systems of Equations by graphing:**

If the appropriate graphs of two equations can be sketched, then the
solutions can be found by

identifying the ordered pair coordinates of each point of intersection. If the
equations can be

solved for y , it is possible to **ENTER** the equations into a calculator and use
the graphing tools to

find the point of intersection.

Steps for a TI -82, 83, 83+, 83+SE, or 84:

Press the **Y =** button and ENTER your equations in the equation editor.
Select a window

that will appropriately graph each of the equations . Press the **GRAPH **button and
look at

the graph. If intersection points do not appear and the graphs do not imply
intersection

points, you can probably stop. If intersection points do not appear but the
graph implies

that intersection points may occur outside your window, then adjust your window.
If

intersection points appear, press **2nd** and **TRACE** to bring up the “CALC” menu and

press **5** for “intersection”. Use the left and right arrow buttons to move your
cursor along

the graph of the first equation to the point of intersection and then press
**ENTER**. You will

then be shifted to the second equation. Press **ENTER** twice more and the
point of

intersection should appear as coordinates along the bottom of your screen.

Steps for a TI -85 or 86:

Press the **GRAPH **and **F1** buttons to open your equation editor—**ENTER** your
equations.

Select a window that will appropriately graph each of the equations. Press the
**GRAPH**

and **F5** buttons to look at the graph. If intersection points do not appear and
the graphs

do not imply intersection points, you can probably stop. If intersection points
do not

appear but the graph implies that intersection points may occur outside your
window,

then adjust your window. If intersection points appear, press the **MORE, F1
**(MATH),

**MORE,** and **F3 **(ISECT) buttons. Use the left and right arrow buttons to move your

cursor along the graph of the first equation to the point of intersection and
then press

**ENTER**. You will then be shifted to the second equation. Press **ENTER** twice more
and

the point of intersection should appear as coordinates along the bottom of your
screen.

Prev | Next |