Question

solving a system of linear equations using the graphing calculator
solve the system of linear equations by graphing
2x + 3y = 16.9
5x = y + 7.4
what is the solution to the system of linear equations? round to the nearest tenth as needed

Explanation:

Step1: Rewrite equations in slope-intercept form

First equation:
$2x + 3y = 16.9$
$3y = -2x + 16.9$
$y = \frac{-2}{3}x + \frac{16.9}{3} \approx -0.7x + 5.6$

Second equation:
$5x = y + 7.4$
$y = 5x - 7.4$

Step2: Set equations equal to each other

$-0.7x + 5.6 = 5x - 7.4$

Step3: Solve for x

$5.6 + 7.4 = 5x + 0.7x$
$13 = 5.7x$
$x = \frac{13}{5.7} \approx 2.3$

Step4: Substitute x to find y

$y = 5(2.3) - 7.4$
$y = 11.5 - 7.4 = 4.1$

Answer:

$(2.3, 4.1)$