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.
\

$$\begin{cases} -3x + 2y = 5 \\\\ 2x - 7y = 8 \\end{cases}$$

(x, y)	is it a solution?
(5, 4)	yes ○ no ○
(-3, -2)	yes ○ no ○
(-7, -8)	yes ○ no ○

Explanation:

Step1: Check (4, 0)

Substitute \(x = 4\), \(y = 0\) into \(-3x + 2y = 5\): \(-3(4)+2(0)=-12
eq5\). So no need to check the second equation.

Step2: Check (5, 4)

Substitute \(x = 5\), \(y = 4\) into \(-3x + 2y\): \(-3(5)+2(4)=-15 + 8=-7
eq5\). So no.

Step3: Check (-3, -2)

Substitute \(x=-3\), \(y = -2\) into \(-3x + 2y\): \(-3(-3)+2(-2)=9 - 4 = 5\). Then into \(2x-7y\): \(2(-3)-7(-2)=-6 + 14 = 8\). Both satisfy. So yes.

Step4: Check (-7, -8)

Substitute \(x=-7\), \(y=-8\) into \(-3x + 2y\): \(-3(-7)+2(-8)=21-16 = 5\). Then into \(2x - 7y\): \(2(-7)-7(-8)=-14 + 56 = 42
eq8\). So no.

Answer:

• For (4, 0): No
• For (5, 4): No
• For (-3, -2): Yes
• For (-7, -8): No