Question

systems of linear equations and inequalities
identifying solutions to a system of linear equations
for each ordered pair, determine whether it is a solution to the system of equations.
\

$$\begin{cases} -18x + 2y = 8 \\\\ y = 9x + 4 \\end{cases}$$

(x, y)	is it a solution?
(3, -5)	\circ	\circ
(-2, -6)	\circ	\circ
(1, 13)	\circ	\circ
(0, 4)	\circ	\circ

Explanation:

Step1: Recall solution definition

A solution to a system of equations satisfies all equations in the system. We'll substitute each ordered pair \((x, y)\) into both equations \(-18x + 2y = 8\) and \(y = 9x + 4\) and check if both are true.

Step2: Check \((3, -5)\)

• Substitute into \(y = 9x + 4\): \(y = 9(3)+4 = 27 + 4 = 31

eq - 5\). So it fails the second equation. No need to check the first.

• Conclusion: Not a solution.

Step3: Check \((-2, -6)\)

• Substitute into \(y = 9x + 4\): \(y = 9(-2)+4=-18 + 4=-14

eq - 6\). Fails the second equation.

• Conclusion: Not a solution.

Step4: Check \((1, 13)\)

• Substitute into \(y = 9x + 4\): \(y = 9(1)+4 = 9 + 4=13\) (satisfies second equation).
• Substitute into \(-18x + 2y = 8\): \(-18(1)+2(13)=-18 + 26 = 8\) (satisfies first equation).
• Conclusion: Is a solution.

Step5: Check \((0, 4)\)

• Substitute into \(y = 9x + 4\): \(y = 9(0)+4 = 0 + 4 = 4\) (satisfies second equation).
• Substitute into \(-18x + 2y = 8\): \(-18(0)+2(4)=0 + 8 = 8\) (satisfies first equation).
• Conclusion: Is a solution.

Answer:

• For \((3, -5)\): No
• For \((-2, -6)\): No
• For \((1, 13)\): Yes
• For \((0, 4)\): Yes