Question

Solve the system of equations: 4x+1=5(x−3y)−6

3(x+6y)+4=9y+19

Answer 1

`((16)/(3),- (1)/(9) )` or
`x=(16)/(3), y=- (1)/(9)`

Explanation:

Hello again!

We are given these two systems:

4x+1=5(x-3y)-6

3(x+6y)+4=9y+19

And we want to solve them for x and y.

First, let's do the distributive property to expand out what is in the parentheses.
4x+1=5(x-3y)-6 --> 4x+1=5x-15y-6

Now simplify 4x+1=5x-15y-6

Subtract 5x from both sides

4x+1=5x-15y-6

-5x -5x

__________

-x+1=-15y-6

Now add 15y to both sides

-x+1=-15y-6

+15y +15y

___________

-x+15y+1=-6

Subtract 1 from both sides

-x+15y=-7

Now for 3(x+6y)+4=9y+19:

3x + 18y + 4 = 9y + 19

Subtract 9y from both sides

3x + 9y + 4 = 19

Subtract 4 from both sides

3x + 9y = 15

Here is our system now:

-x+15y=-7

3x+9y=15

On 3x+9y=15, because all of the values are multiples of 3, we can actually divide it by 3.

3x+9y=15

÷3 ÷3

x + 3y = 5

So here it is again:

-x+15y=-7

x+3y=5

These equations can actually be solved using elimination! We will be adding these equations together to clear out a variable, solve for the uncleared variable, and then use the value of the uncleared variable to find the value of the cleared variable

So, add -x+15y=-7 and x+3y=5 together.

-x+15y=-7
+

x+3y=5

_____

18y=-2

Divide both sides by 18

y=
`-(1)/(9)`

Now substitute -1/9 as y into either -x+15y=7 or x+3y=5

Taking x+3y=5 for example,

x+3(-1/9)=5

multiply

x-1/3+5

Add 1/3 to both sides

x=5+1/3=16/3

So the answer is
`x=(16)/(3) , y=-(1)/(9)`, or as a point,
`((16)/(3),- (1)/(9) )`

Hope this helps!