alishacherevko
contestada

What is the solution of the system? Use the substitution method.

3x + 2y =11
x − 2 = −4y

A.The only solution is (12, −52) .

B. The only solution is (4, −12) .

C. There is no solution.

D. There are an infinite number of solutions.

Respuesta :

ilovecats9573ozkvsq
Start by isolating one of the variables
x=-4y+2
Sub x into the other formula and solve for the y value of the solution.
3(-4y+2)+2y=11
-12y+6+2y=11
-12y+2y=11-6
-10y=5
y=-1/2
Sub the y value into the x formula you created.
x=-4(-1/2)+2
x=2+2
x=4
Therefore the solution is (4,-1/2) I think the answer is B unless the y value is actually -12.
Hope this helps :)
boffeemadrid

The solution of the given system is required.

The correct option is B. The only solution is [tex]\left(4,-\dfrac{1}{2}\right)[/tex]

The system is

[tex]3x+2y=11[/tex]

[tex]x-2=-4y\\\Rightarrow x=-4y+2[/tex]

Substituting x value in the first equation

[tex]3(-4y+2)+2y=11\\\Rightarrow -12y+6+2y=11\\\Rightarrow y=\dfrac{11-6}{-12+2}\\\Rightarrow y=-\dfrac{1}{2}[/tex]

Finding x

[tex]x=-4y+2=-4\times -\dfrac{1}{2}+2\\\Rightarrow x=4[/tex]

The only solution is [tex]\left(4,-\dfrac{1}{2}\right)[/tex]

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