Answer:
[tex](\frac{16}{3},- \frac{1}{9} )[/tex] or [tex]x=\frac{16}{3}, y=- \frac{1}{9}[/tex]
Step-by-step 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=[tex]-\frac{1}{9}[/tex]
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 [tex]x=\frac{16}{3} , y=-\frac{1}{9}[/tex], or as a point, [tex](\frac{16}{3},- \frac{1}{9} )[/tex]
Hope this helps!
