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.
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Explanation:

Step1: Rewrite equations in slope-intercept form

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

Second equation: $5x = y + 7.4$
Rearrange to solve for $y$:
$y = 5x - 7.4$

Step2: Set equations equal to each other

To find the $x$-coordinate of the intersection, set the two expressions for $y$ equal:
$5x - 7.4 = -\frac{2}{3}x + \frac{16.9}{3}$

Step3: Solve for $x$

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

Step4: Substitute $x$ to find $y$

Use $y = 5x - 7.4$:
$y = 5(2.3) - 7.4 = 11.5 - 7.4 = 4.1$

Answer:

$(2.3, 4.1)$