Question

estimate the solution to the system of equations. you can use the interactive graph below to find the solution. \\(\

$$\begin{cases} -3x + 3y = 9 \\\\ 2x - 7y = -14 \\end{cases}$$

\\) choose 1 answer: a \\(x = -1\frac{2}{5}, y = 2\frac{3}{5}\\) b \\(x = -2\frac{2}{5}, y = 2\frac{3}{5}\\) c \\(x = -1\frac{2}{5}, y = 1\frac{3}{5}\\) d \\(x = -2\frac{2}{5}, y = 1\frac{3}{5}\\)

Explanation:

Step1: Simplify first equation

Divide first equation by 3:
$-x + y = 3$
Rearrange to solve for $y$:
$y = x + 3$

Step2: Substitute $y$ into second equation

Substitute $y=x+3$ into $2x - 7y = -14$:
$2x - 7(x + 3) = -14$
Expand and simplify:
$2x -7x -21 = -14$
$-5x -21 = -14$

Step3: Solve for $x$

Isolate $-5x$:
$-5x = -14 + 21$
$-5x = 7$
Solve for $x$:
$x = -\frac{7}{5} = -1\frac{2}{5}$

Step4: Solve for $y$

Substitute $x=-\frac{7}{5}$ into $y=x+3$:
$y = -\frac{7}{5} + 3 = -\frac{7}{5} + \frac{15}{5} = \frac{8}{5} = 1\frac{3}{5}$

Answer:

C. $x = -1\frac{2}{5}, y = 1\frac{3}{5}$