Question

Consider the following system of equations made up of Lines 1 and 2.

Answer 1

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 $6 x-7 y=25$

Let us substitute the coordinate (0,3) in Line 1, we get,

$\begin{array}{r}{6(0)-7(3)=25} \\{-21=25}\end{array}$

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 $2 x+9 y=-3$

Let us substitute the coordinate (0,0) in Line 2, we get,

$\begin{array}{r}{2(0)+9(0)=-3} \\{0=-3}\end{array}$

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 $2 x+9 y=-3$

Let us substitute the coordinate (-6,1), in Line 2, we get,

$\begin{array}{r}{2(-6)+9(1)=-3} \\{-12+9=-3} \\{-3=-3}\end{array}$

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,

$\begin{array}{r}{6(3)-7(-1)=25} \\{18+7=25} \\{25=25}\end{array}$

Substituting (3,-1) in line 2, we have,

$\begin{array}{r}{2(3)+9(-1)=-3} \\{6-9=-3} \\{-3=-3}\end{array}$

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,

$\begin{array}{r}{6(3)-7(1)=25} \\{18-7=25} \\{11=25}\end{array}$

Substituting (3,1) in line 2, we have,

$\begin{array}{r}{2(3)+9(1)=-3} \\{6+9=-3} \\{15=-3}\end{array}$

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.