Question

graph $y = 3x - 6$ by plotting the $y$-intercept at $(0, -6)$. use the slope of 3 to count up 3 spaces and to the right 1 space to plot the second point. graph $y = \frac{2}{5}x + 5$ by plotting the $y$-intercept at $(0, 5)$. use the slope of $\frac{2}{5}$ to count up 2 spaces and to the right 5 spaces to plot the second point. what is the estimated solution of the system? enter your answer in the box. round each coordinate to the nearest integer.

Explanation:

Step1: Set equations equal

$3x - 6 = \frac{2}{5}x + 5$

Step2: Eliminate fraction, multiply by 5

$15x - 30 = 2x + 25$

Step3: Isolate x terms

$15x - 2x = 25 + 30$
$13x = 55$

Step4: Solve for x

$x = \frac{55}{13} \approx 4.23$

Step5: Substitute x to find y

$y = 3(4.23) - 6 = 12.69 - 6 = 6.69$

Step6: Round to nearest integer

$x \approx 4$, $y \approx 7$

Answer:

$(4, 7)$