solving a system of linear equations using the graphing calculator\nsolve the system of linear equations by…

Explanation:

Step1: Rewrite the equations in slope - intercept form ($y = mx + b$)

For the first equation (2x+3y = 16.9): [ \begin{align*} 3y&=-2x + 16.9\ y&=-\frac{2}{3}x+\frac{16.9}{3}\ y&=-\frac{2}{3}x + 5.633\cdots \end{align*} ] For the second equation (5x=y + 7.4): [ \begin{align*} y&=5x-7.4 \end{align*} ]

Step2: Use a graphing calculator

Input the two functions (y =-\frac{2}{3}x + 5.633\cdots) and (y = 5x-7.4) into the graphing calculator. The intersection point of the two lines is the solution of the system of equations. When we use a graphing calculator (or solve the system algebraically by setting (-\frac{2}{3}x+5.633\cdots=5x - 7.4)): [ \begin{align*} -\frac{2}{3}x+5.633\cdots&=5x-7.4\ -\frac{2}{3}x-5x&=-7.4 - 5.633\cdots\ -\frac{2x+15x}{3}&=-13.033\cdots\ -\frac{17x}{3}&=-13.033\cdots\ x&=\frac{- 13.033\cdots\times3}{-17}\ x&=\frac{-39.1}{-17}\ x& = 2.3 \end{align*} ] Substitute (x = 2.3) into (y = 5x-7.4) [ y=5\times2.3-7.4=11.5 - 7.4=4.1 ]

Answer:

((2.3,4.1))