Question

Solve the system by the substitution method. -12x - 2y = -4 6x + 3y = 18

Answer 1

Answer: x = -1 , y = 8✔️

Step-by-step explanation:

-12x - 2y = -4 } Equation 1

6x + 3y = 18 } Equation 2

We can extract the value of x from the equation 2:

6x + 3y = 18 } Equation 2

6x = 18 - 3y

x = (18 - 3y)/6 } Equation 2

Then we can substitute this value of x in equation 1:

-12x - 2y = -4 } Equation 1

-12·(18 - 3y)/6 - 2y = -4

-36 + 6y -2y = -4

4y = -4 + 36

4y = 32

y = 32/4 = 8

Now we can substitute this value of y in equation 2:

x = (18 - 3y)/6 } Equation 2

x = (18 - 3·8)/6 = (18 -24)/6 = -6/6 = -1

Answer: x = -1 , y = 8✔️

Check

We can check this result by substituting these values of x and y into the equations:

-12x - 2y = -4 } Equation 1  

-12·(-1) - 2·8 = -4 ► 12 - 16 = -4✔️ checked!

6x + 3y = 18 } Equation 2

6·(-1) + 3·8 = 18 ► -6 + 24 = 18✔️ checked!

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