Question

solve the system by substitution. if the system is inconsistent or has dependent equations, say so.$4x - 5y = -20$$x + 6y = 53$select the correct choice below and, if necessary, fill in the answer box to complete your choice.a. the solution set is {5,8}(type an ordered pair. simplify your answer.)b. the system has dependent equations. the solution set is {(x,y)| x + 6y = 53}.c. the system is inconsistent. the solution set is the empty set.

Explanation:

Step1: Isolate $x$ from second equation

$x = 53 - 6y$

Step2: Substitute $x$ into first equation

$4(53 - 6y) - 5y = -20$

Step3: Expand and simplify for $y$

$212 - 24y - 5y = -20$
$212 - 29y = -20$
$-29y = -232$
$y = \frac{-232}{-29} = 8$

Step4: Substitute $y=8$ to find $x$

$x = 53 - 6(8) = 53 - 48 = 5$

Answer:

A. The solution set is $\{(5,8)\}$