Question

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

$$\begin{cases} 3x - 2y = -5 \\\\ 5x + 4y = -1 \\end{cases}$$

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

Explanation:

Step1: Check (-1,1)

Substitute \(x = -1\), \(y = 1\) into \(3x - 2y\): \(3(-1)-2(1)=-3 - 2=-5\) (matches first equation). Substitute into \(5x + 4y\): \(5(-1)+4(1)=-5 + 4=-1\) (matches second equation). So (-1,1) is a solution.

Step2: Check (3,-4)

Substitute \(x = 3\), \(y = -4\) into \(3x - 2y\): \(3(3)-2(-4)=9 + 8 = 17
eq -5\). So (3,-4) is not a solution.

Step3: Check (-7,-8)

Substitute \(x = -7\), \(y = -8\) into \(3x - 2y\): \(3(-7)-2(-8)=-21 + 16=-5\) (matches first equation). Substitute into \(5x + 4y\): \(5(-7)+4(-8)=-35 - 32=-67
eq -1\). So (-7,-8) is not a solution.

Step4: Check (5,0)

Substitute \(x = 5\), \(y = 0\) into \(3x - 2y\): \(3(5)-2(0)=15
eq -5\). So (5,0) is not a solution.

Answer:

For \((-1, 1)\): Yes
For \((3, -4)\): No
For \((-7, -8)\): No
For \((5, 0)\): No