Question

solving a system of linear equations using the graphing calculator
solve the system of linear equations by graphing round the solution to the nearest tenth as needed
$y + 2.3 = 0.45x$
$-2y = 4.2x - 7.8$
$\circ$ $(2.4, -1.2)$
$\circ$ $(-1, 2.5)$
$\circ$ no solution
$\circ$ infinitely many solutions

Explanation:

Step1: Rewrite first equation to slope-intercept form

Rearrange $y + 2.3 = 0.45x$ to solve for $y$:
$y = 0.45x - 2.3$

Step2: Rewrite second equation to slope-intercept form

Divide $-2y = 4.2x - 7.8$ by $-2$:
$y = \frac{4.2}{-2}x + \frac{-7.8}{-2}$
$y = -2.1x + 3.9$

Step3: Set equations equal to find $x$

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

Step4: Substitute $x$ to find $y$

Plug $x \approx 2.4$ into $y = 0.45x - 2.3$:
$y = 0.45(2.4) - 2.3$
$y = 1.08 - 2.3 = -1.22 \approx -1.2$

Answer:

(2.4, -1.2)