Question

understanding check: solve using substitution. check your solution. a. \\(\

$$\begin{cases} y - 2 = -2x \\\\ 3x - 17 = 2y \\end{cases}$$

\\)

Explanation:

Step1: Isolate $y$ in first equation

$y = -2x + 2$

Step2: Substitute $y$ into second equation

$3x - 17 = 2(-2x + 2)$

Step3: Expand and simplify the equation

$3x - 17 = -4x + 4$
$3x + 4x = 4 + 17$
$7x = 21$

Step4: Solve for $x$

$x = \frac{21}{7} = 3$

Step5: Substitute $x=3$ into $y=-2x+2$

$y = -2(3) + 2 = -6 + 2 = -4$

Step6: Verify solution in both equations

First equation: $-4 - 2 = -2(3) \implies -6 = -6$ (True)
Second equation: $3(3) - 17 = 2(-4) \implies 9 - 17 = -8 \implies -8 = -8$ (True)

Answer:

$x=3$, $y=-4$