Question

is (3, 8) a solution to this system of equations?
$y = \frac{5}{3}x + 3$
$y = \frac{7}{3}x + 1$
options: yes, no

Explanation:

Step1: Check first equation

Substitute \(x = 3\), \(y = 8\) into \(y=\frac{5}{3}x + 3\).
Right - hand side: \(\frac{5}{3}\times3+3=5 + 3=8\).
Left - hand side: \(y = 8\). So, \((3,8)\) satisfies the first equation.

Step2: Check second equation

Substitute \(x = 3\), \(y = 8\) into \(y=\frac{7}{3}x + 1\).
Right - hand side: \(\frac{7}{3}\times3+1=7 + 1=8\).
Left - hand side: \(y = 8\). So, \((3,8)\) satisfies the second equation.

Answer:

yes