Solve the system of linear equations by graphing calculator

How do I use a graph to solve a system of linear equations on the TI-84 Plus C Silver Edition calculator?

To solve a system of linear equations using a graph on the TI-84 Plus C Silver Edition, follow the example below. The purpose is to solve a system of two equations and two unknowns.

Example: Using a graph, find the solution for the equations y = 2x + 7 and y = -3x - 8.

1) Press [Y=] to access the Y= editor.
2) For Y1, input 2X+7.
3) For Y2 input -3X-8.

4) Press [GRAPH] to graph the equations.
5) Press [2nd] [TRACE] [5] to select the "intersect" command from the CALC menu.
6) The handheld will prompt for the "First curve" which means it wants the user to select the first equation. Press [ENTER] to mark the first equation.

Please Note: Either the Y1 equation or the Y2 equation can be marked as the first equation.

7) The handheld will prompt for the "Second curve" which means it wants the user to select the second equation. The handheld should also automatically jump to the second equation. Press [ENTER] to mark the second equation.
8) The handheld will prompt for the "Guess?" which means it wants the user to take a guess at the solution. Using the [◄] and [►] keys, move the cursor as close as possible to the intersection point (which is the solution) and press [ENTER]. The handheld will display the solutions for both the X and Y variables as a coordinate point (-3,1).

9) To check the accuracy of the solution, access the TABLE by pressing [2nd] [GRAPH]. From the X column, use the [▼] and [▲] keys to scroll and locate the value (-3). When X=-3, both Y1 and Y2 are equal to 1 which means the solution is accurate.

Please see the TI-84 Plus C Silver Edition guidebook for additional information.

How to Use a Graphing Calculator to Solve an Advanced System of Linear Equations

Step 1: Make sure the linear equations are in the form of y = mx + b. If the x term or the constant term is on the side of y, add the opposite of the term on both sides so that y is the only term on the left side.

Step 2: Now, on the calculator, press [y=].

Step 3: Enter the first equation at "Y1= ". Press [enter].

Step 4: Enter the second equation at "Y2= ". Press [enter].

Step 5: Press [2nd][trace].

Step 6: Using the arrow keys, come down to "5:intersect". Press [enter].

Step 7: The graphs of the equations are drawn on the window. On the top part of the window, the first equation is displayed. On the bottom part, it asks "First curve?". Press [enter].

Step 8: Now, the second equation is displayed and it asks "Second curve?". Press [enter].

Step 9: On the bottom part, it asks "Guess?". Press [enter].

Step 10: The coordinates of the intersecting point, which is the solution to the system of the linear equations, are displayed "X= " and "Y= ".

How to Use a Graphing Calculator to Solve an Advanced System of Linear Equations Vocabulary

System of linear equations

A system of linear equations is two or more linear equations using the same set of variables.

Let's use these steps, formulas, and definitions to work through two examples on using a graphing calculator to solve an advanced system of linear equations.

How to Use a Graphing Calculator to Solve an Advanced System of Linear Equations: Example 1

Use a graphing calculator to solve the following system of linear equations: {eq}y=0.15x -0.12, \ 2.5x - y=- 2.4 {/eq}.

Step 1: Make sure the linear equations are in the form of y = mx + b. We can see that {eq}2.5x - y = 2.4 {/eq} is not in the slope-intercept form. Using the properties of equality and commutative property of addition, change the form of the equation.$$\begin{align} 2.5x - y &=- 2.4 \\\\ 2.5x - y + 2.5x & = -2.4 + 2.5x \\\\ -y &= 2.5x - 2.4 \\\\ y & = -2.5x + 2.4 \\\\ \end{align} $$

Step 2: Now, on the calculator, press [y=].

Step 3: Enter the first equation at "Y1= -0.15x-0.12 ". Press [enter].

Step 4: Enter the second equation at "Y2=-2.5x+2.4 ". Press [enter].

Step 5: Press [2nd][trace].

Step 6: Using the arrow keys, come down to "5:intersect". Press [enter].

Step 7: We see the lines for the equations being drawn. On the top part of the window, the first equation is displayed. On the bottom part, it asks "First curve?". Press [enter].

Step 8: Now the second equation is displayed and it asks "Second curve?". Press [enter].

Step 9: On the bottom part, it asks "Guess?". Press [enter].

Step 10: The coordinates of the intersecting point, which is the solution to the system of the linear equations, are displayed "X=1.0723404" and "Y=-.2808511".

Equation View

Graph View

How to Use a Graphing Calculator to Solve an Advanced System of Linear Equations: Example 2

Use a graphing calculator to solve the following system of linear equations: {eq}y=1.2x - 2.47, \ \ -3.01x + y= 3.9 {/eq}.

Step 1: Make sure the linear equations are in the form of Y = mx + b. The current equation {eq}-3.01x + y = 3.9 {/eq} is not in the slope-intercept form. Using the properties of equality and commutative property of addition, change the form of the equation. $$\begin{align} -3.01x + y &= 3.9 \\\\ y &= 3.01x + 3.9 \\\\ \end{align} $$

Step 2: Now, on the calculator, press [y=].

Step 3: Enter the first equation at "Y1= 1.2x - 2.47". Press [enter].

Step 4: Enter the second equation at "Y2= 3.01x + 3.9". Press [enter].

Step 5: Press [2nd][trace].

Step 6: Using the arrow keys, come down to "5:intersect". Press [enter].

Step 7: We see the lines for the equations being drawn. On the top part of the window, the first equation is displayed. On the bottom part, it asks "First curve?". Press [enter].

Step 8: Now, the second equation is displayed and it asks "Second curve?". Press [enter].

Step 9: On the bottom part, it asks "Guess?". Press [enter].

Step 10: The coordinates of the intersecting point, which is the solution to the system of the linear equations, are displayed "X=-3.519337" and "Y=-6.693204".

Equation View

Graph View

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