Question

answer the following based on solving the given system of equations by using the substitution method.
$3x - 2y = 6$
$x - 4y = -8$
part a: which variable in which equation would be best (easiest) to isolate?
part b: if you isolate the variable you chose in part a, what would this new equation be?
part c: what is the solution to this system? be sure to type the full ordered pair and do not use the space bar.

Explanation:

Step1: Choose easiest variable to isolate

The second equation $x - 4y = -8$ has $x$ with a coefficient of 1, so it is easiest to isolate $x$ from this equation.

Step2: Isolate $x$ from the second equation

Add $4y$ to both sides:
$x = 4y - 8$

Step3: Substitute $x$ into first equation

Replace $x$ in $3x - 2y = 6$ with $4y - 8$:
$3(4y - 8) - 2y = 6$

Step4: Simplify and solve for $y$

Expand and combine like terms:
$12y - 24 - 2y = 6$
$10y - 24 = 6$
Add 24 to both sides:
$10y = 30$
Divide by 10:
$y = 3$

Step5: Substitute $y=3$ into isolated $x$

$x = 4(3) - 8 = 12 - 8 = 4$

Answer:

Part A: $x$ in the second equation $x - 4y = -8$
Part B: $x = 4y - 8$
Part C: $(4,3)$