Option B: The ordered pair (-3,3) is the solution to the system of equations.
Explanation:
The system of equations are [tex]3x+5y=6[/tex] and [tex]4x+2y=-6[/tex]
We need to determine the solution to the system of equations.
Let us solve the system of equations using substitution method.
From the equation [tex]4x+2y=-6[/tex] , let us determine the value of y.
[tex]2y=-6-4x[/tex]
[tex]y=-3-2x[/tex]
Substituting the value [tex]y=-3-2x[/tex] in the equation [tex]3x+5y=6[/tex], we get,
[tex]3x+5(-3-2x)=6[/tex]
Simplifying, we get,
[tex]3x-15-10x=6[/tex]
[tex]-15-7x=6[/tex]
[tex]-7x=21[/tex]
[tex]x=-3[/tex]
Thus, the value of x is -3
Substituting [tex]x=-3[/tex] in the equation [tex]4x+2y=-6[/tex], we get,
[tex]4(-3)+2y=-6[/tex]
[tex]-12+2y=-6[/tex]
[tex]2y=6[/tex]
[tex]y=3[/tex]
Thus, the value of y is 3
Thus, the solution to the system of equations is (-3,3)
Hence, Option B is the correct answer.
