Question

solve the system of linear equations by graphing. round the solution to the nearest tenth as needed.\\( y + 2.3 = 0.45x \\)\\( -2y = 4.2x - 7.8 \\)\\( \bigcirc\\ (2.4, -1.2) \\)\\( \bigcirc\\ (-1, 2.5) \\)\\( \bigcirc\\ \text{no solution} \\)\\( \bigcirc\\ \text{infinitely many solutions} \\)

Explanation:

Step1: Rewrite to slope-intercept form

First equation: $y = 0.45x - 2.3$
Second equation: $y = -2.1x + 3.9$

Step2: Set equations equal

$0.45x - 2.3 = -2.1x + 3.9$

Step3: Solve for x

$0.45x + 2.1x = 3.9 + 2.3$
$2.55x = 6.2$
$x = \frac{6.2}{2.55} \approx 2.4$

Step4: Substitute x to find y

$y = 0.45(2.4) - 2.3$
$y = 1.08 - 2.3 = -1.22 \approx -1.2$

Answer:

(2.4, -1.2)