Question

problem 10 show your work to get full credit
on the set of axes below, graph the equation
3y + 2x = 15.

graph of coordinate axes

explain why (-6,9) is a solution to the equation.

Explanation:

Step1: Recall solution definition

A solution \((x,y)\) satisfies the equation when substituted.

Step2: Substitute \(x = -6\), \(y = 9\)

Substitute into \(3y + 2x = 15\):
Left - hand side (LHS) \(= 3(9)+2(-6)\)
\(= 27 - 12\)
\(= 15\)
Right - hand side (RHS) \(= 15\)
Since LHS = RHS, \((-6,9)\) satisfies the equation.

Answer:

To determine if \((-6,9)\) is a solution, substitute \(x = -6\) and \(y = 9\) into \(3y + 2x = 15\). Calculating the left - hand side: \(3(9)+2(-6)=27 - 12 = 15\), which equals the right - hand side (\(15\)). So \((-6,9)\) is a solution as it satisfies the equation.