The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for the system of equations that has the solution which corresponds to a point at (6, -2)?
Responses
A 13
x + 4y = −41 3 x + 4y = −4
B 13
x + 3y = 41 3 x + 3y = 4
C 13
x + 2y = −21 3 x + 2y = −2
D 13
x + 2y = 2
C. 13x + 2y = -2. The point (6, -2) satisfies the equation 3x + 2y = -2 when x=6 and y=-2. This is the second linear equation for the system.
To determine the second linear equation for the system of equations that has the solution (6, -2), we need to find the equation that passes through the point (6, -2).
Looking at the given options:
A) 13x + 4y = -41
B) 13x + 3y = 41
C) 13x + 2y = -21
D) 13x + 2y = 2
We can substitute the values x = 6 and y = -2 into each equation and see which one satisfies the equation.
Substituting (6, -2) into option A:
13(6) + 4(-2) = -41
78 - 8 = -41
70 ≠ -41
Substituting (6, -2) into option B:
13(6) + 3(-2) = 41
78 - 6 = 41
72 ≠ 41
Substituting (6, -2) into option C:
13(6) + 2(-2) = -21
78 - 4 = -21
74 ≠ -21
Substituting (6, -2) into option D:
13(6) + 2(-2) = 2
78 - 4 = 2
74 ≠ 2
None of the given options satisfy the equation with the point (6, -2). Therefore, there is no correct answer among the provided options.