Y=6x-11 -3x-2y=7   solve by substitution

Expert Answers
uwais17 eNotes educator| Certified Educator

When simplifying  equations that are done simultaneously it is important to make one variable the subject of the formula to simplify solving the equations. 

We already have y the subject of the formula of the one equation:

`y = 6x -11`

Now we can make y the subject of the formula for the next equation: 

`-3x -2y = 7`

`-3x-7 =2y` (apply inverse operations)

`(-3x-7)/2 = y` (apply inverse operations)

Since we have two equations, we can now equate the two equations and solve for x: 

`6x - 11 = (-3x-7)/2`

`2(6x -11) = -3x -7` (inverse operations)

`12x - 22 = -3x -7` (multiply out)

Now get the variable x on the one side, and the constants on the other side:

`12x + 3x = -7+22` (apply inverse operations)

`15x = 15`

`x =1`

Since we know what x is, we can substitute it in the first equation as it is the easiest equation: 

`y = 6(1) -11`

`y = -5`

SUMMARY: `x = 1, y =-5`

himanshukr1999 | Student

Y=6X-11 &-3X-2Y=7

Y is the subject of formula in the first eqn.

So, substitute its value in the second eqn:-

-3x-2(6x-11)=7......this becomes a linear eqn in x, So solving this, we get,

-3x-12x+22=7

-15x+22=7

22-7=15x...transposing

Hence, x turns out to be 1

Place this value in the 1st eqn

Y=6(1)-11

Thus, y=-5

To check for validity place the values in the original eqn, and see whether it satisfies both the eqn .