Example. Use a graphing calculator to solve the system of equations x - y = 2, 2x + 3y = 6.
Solution: The following is for a TI-92 Graphing Calculator.

Solve each equation for y: (1) y = x - 2, (2) y = (- 2/3)x +2.

Graph both functions. (Hint: Let xmin= - 5, xmax= 5, ymin= - 5, ymax= 5)

From the Graph screen press  5 (Intersection). (Note question in lower left corner of the screen.)

Select the first curve (place the cursor on it) by using  or  then press  .

Select the second curve:  or   .

Set the lower bound for x. Type a value (or use  or  staying left of the intersection point): 1 

Set the upper bound for x. Type a value (or use  or  staying right of the intersection point): 3 

7. Algebraic Solution of a Linear System

A graphing calculator may be used in the algebraic solution of a linear system. The substitution method is utilized.

Example. Use a graphing calculator to solve the system x - 2y = 5, 2x + y = 0.

Solution: Display and clear the Home screen:    8

Clear the entry line: 

Solve the first equation for x:  1 (Solve) x  2y  5  x  

The solution is at the lower right of the history area: x = 2y + 5

Start the solution of the second equation for y, do not press  at this time:

1 2x  y  0  y 

Continue on the entry line:  

Press:  (this gives the value of y in the history area: y = - 2

Next we highlight the x equation in the history area and ‘paste’ it on the entry line:   

This equation is to be evaluated with the value of y in the history area:       Another press of  displays x =1 in the history area.

Problem. Use a graphing calculator to solve the system x + y = 1, x - 2y = - 7.
 

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