Question

solving systems of equations with substitution
solve the system of equations by substitution.
\\(\frac{5}{8}x + \frac{1}{3}y = \frac{17}{24}\\)
\\(x + 7y = 8\\)
( , )

Explanation:

Step1: Isolate x from second equation

$x = 8 - 7y$

Step2: Substitute x into first equation

$\frac{3}{8}(8 - 7y) + \frac{1}{3}y = \frac{17}{24}$

Step3: Simplify left-hand side

$3 - \frac{21}{8}y + \frac{1}{3}y = \frac{17}{24}$

Step4: Combine like terms for y

$3 - \frac{63y - 8y}{24} = \frac{17}{24}$
$3 - \frac{55}{24}y = \frac{17}{24}$

Step5: Solve for y

$-\frac{55}{24}y = \frac{17}{24} - 3$
$-\frac{55}{24}y = \frac{17 - 72}{24}$
$-\frac{55}{24}y = -\frac{55}{24}$
$y = 1$

Step6: Substitute y=1 into x=8-7y

$x = 8 - 7(1) = 1$

Answer:

$(1, 1)$