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)
