Option c: (-6,1) is a solution for Line 2 only
Option d: (3,-1) is a solution to the system
Explanation:
Option a: (0,3) is a solution for Line 1 only
Line 1 is [tex]6 x-7 y=25[/tex]
Let us substitute the coordinate (0,3) in Line 1, we get,
[tex]\begin{array}{r}{6(0)-7(3)=25} \\{-21=25}\end{array}[/tex]
Since, both sides of the equation are not equal, the coordinate (0,3) cannot be a solution to Line 1.
Thus, Option a is not the correct answer.
Option b: (0,0) is a solution for Line 2 only.
Line 2 is [tex]2 x+9 y=-3[/tex]
Let us substitute the coordinate (0,0) in Line 2, we get,
[tex]\begin{array}{r}{2(0)+9(0)=-3} \\{0=-3}\end{array}[/tex]
Since, both sides of the equation are not equal, the coordinate (0,0) cannot be a solution to Line 2.
Thus, Option b is not the correct answer.
Option c: (-6,1) is a solution for line 2 only.
Line 2 is [tex]2 x+9 y=-3[/tex]
Let us substitute the coordinate (-6,1), in Line 2, we get,
[tex]\begin{array}{r}{2(-6)+9(1)=-3} \\{-12+9=-3} \\{-3=-3}\end{array}[/tex]
Since, both sides of the equation are equal, the coordinate (-6,1) is a solution for line 2 only.
Thus, Option c is the correct answer.
Option d: (3,-1) is a solution to the system
Let us substitute the coordinate (3,-1) in line 1 and line 2, we get,
In line 1, we have,
[tex]\begin{array}{r}{6(3)-7(-1)=25} \\{18+7=25} \\{25=25}\end{array}[/tex]
Substituting (3,-1) in line 2, we have,
[tex]\begin{array}{r}{2(3)+9(-1)=-3} \\{6-9=-3} \\{-3=-3}\end{array}[/tex]
Since, from line 1 and line 2, both sides of the equation are equal, the coordinate (3,-1) is a solution to the system.
Thus, Option d is the correct answer.
Option e: (3,1) is a solution to the system
Let us substitute the coordinate (3,1) in line 1 and line 2, we get,
In line 1, we have,
[tex]\begin{array}{r}{6(3)-7(1)=25} \\{18-7=25} \\{11=25}\end{array}[/tex]
Substituting (3,1) in line 2, we have,
[tex]\begin{array}{r}{2(3)+9(1)=-3} \\{6+9=-3} \\{15=-3}\end{array}[/tex]
Since, from line 1 and line 2, both sides of the equation are not equal, the coordinate (3,1) is a solution to the system.
Thus, Option e is not the correct answer.
