Answer:
They are the only values that make the equation true
Step-by-step explanation:
Equation A = [tex]-2y +6x=12[/tex]
Equation B: [tex]4x+12y=-12[/tex]
Intersection point (1.5,-1.5)
Option A. They satisfy equation A but not equation B
[tex]-2y +6x=12[/tex]
Substitute x = 1.5 and y = -1.5
[tex]-2(-1.5) +6(1.5)=12[/tex]
[tex]12=12[/tex]
Satisfied Equation A
[tex]4x+12y=-12[/tex]
Substitute x = 1.5 and y = -1.5
[tex]4(1.5)+12(-1.5)=-12[/tex]
[tex]-12=-12[/tex]
Satisfied Equation B
Thus Option A is Wrong.
Option B. They satisfy equation B but not equation A
Option B is wrong Proved Above
Option C : They are the only values that make the equation true
Since they are satisfying both the equations
Hence Option C is true.
Option D. They show that the lines are perpendicular
[tex]y = mx+c[/tex]
Where m is the slope
Equation A = [tex]-2y +6x=12[/tex]
[tex]6x-12=2y[/tex]
[tex]\frac{6x-12}{2}=y[/tex]
[tex]3x-6=y[/tex]
Thus the slope of equation A is 3
[tex]4x+12y=-12[/tex]
[tex]4x-12=-12y[/tex]
[tex]\frac{4x-12}{-12}=y[/tex]
[tex]\frac{-x}{3}+1=y[/tex]
Slope of equation B is [tex]\frac{-1}{3}[/tex]
Two Lines are perpendicular if their slopes are same
Thus Option D is wrong since slopes are different .
Hence Option C is true:They are the only values that make the equation true
