Question

1. \\( y = x - 4 \\)\\( -4x - 6y = -16 \\)step 1: substitute \\( y = \underline{quadquad} \\)step 2: equation becomes: \underline{quadquad}step 3: solve for \\( x = \underline{quadquad} \\)step 4: find \\( y = \underline{quadquad} \\)solution: (\underline{quadquad}, \underline{quadquad})

Explanation:

Step1: Substitute y expression

Substitute $y = x-4$ into the second equation.

Step2: Rewrite the equation

$-4x - 6(x-4) = -16$
Expand and simplify:
$-4x -6x +24 = -16$
$-10x +24 = -16$

Step3: Solve for x

Isolate the x term:
$-10x = -16 -24$
$-10x = -40$
$x = \frac{-40}{-10} = 4$

Step4: Find y using x value

Substitute $x=4$ into $y=x-4$:
$y = 4 - 4 = 0$

Answer:

Step 1: $x-4$
Step 2: $-4x - 6(x-4) = -16$ (simplified to $-10x +24 = -16$)
Step 3: $4$
Step 4: $0$
Solution: $(4, 0)$