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Solve systems of equations by substitution for x-2y= -8 and 6x+7y=9

Sagot :

SenorMathWiz

Answer:

(-2,3)

Step-by-step explanation:

In order to solve the system using substitution, one of the variables must be defined so we can substitute it into the other equation.

We can easily define x in the second first by adding 2y from both sides

x - 2y = - 8

* add 2y to both sides *

x = 2y - 8

Now that we have defined x in the first equation we can plug in the defined value of x into the second equation

6x + 7y = 9

substitute 2y - 8 for x

6 (2y - 8) + 7y = 9

distribute 6 to -2y and -8

6 * 2y = 12y

6 * -8 = -48

12y - 48 + 7y = 9

combine like terms ( 12y + 7y = 19y )

19y - 48 = 9

add 48 to both sides

19y = 57

divide both sides by 19

19y/19 = y and 57/19 = 3

we're left with y = 3

Now that we have found the value of one of the variables we can plug it in to one of the equations ( note that plugging the value of y and solving for x in either equation will lead us to the same answer ) and solve for the other variable (x)

x - 2y = -8

y = 3

x - 2(3) = -8

multiply -2 and 3

x - 6 = -8

add 6 to both sides

x = -2

so x = -2 and y= 3

Therefore the solution to the system of equations is (-2,3)

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