Question

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 to 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

$\frac{-2}{3}x + \frac{16.9}{3} = 5x - 7.4$

Step3: Solve for x

Multiply all terms by 3 to eliminate denominators:
$-2x + 16.9 = 15x - 22.2$
$16.9 + 22.2 = 15x + 2x$
$39.1 = 17x$
$x = \frac{39.1}{17} \approx 2.3$

Step4: Substitute x to find y

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

Answer:

$(2.3, 4.1)$