Question

solve the system by substitution.
$y = 4x - 9$
$-7x - 6y = -39$

Explanation:

Step1: Substitute $y=4x-9$ into second equation

$-7x - 6(4x - 9) = -39$

Step2: Expand and simplify the equation

$-7x -24x + 54 = -39$
$-31x + 54 = -39$

Step3: Isolate the $x$-term

$-31x = -39 - 54$
$-31x = -93$

Step4: Solve for $x$

$x = \frac{-93}{-31} = 3$

Step5: Substitute $x=3$ into $y=4x-9$

$y = 4(3) - 9$

Step6: Calculate the value of $y$

$y = 12 - 9 = 3$

Answer:

$x=3$, $y=3$