what coordinate point is the solution to the system?
{3x+2y=8
{x-y=1
y=x-1 so 3x+2(x-1)=8
3x+2x-2=8
5x-2=8
5x=10
- -
5 5
x=2
Then 2-y=1
-2 -2
-y=-1
y=1
Well, to cut the crap the answer is (2,1)
To find the coordinate point that is the solution to the system of equations, we can start by solving the first equation for y. Given the equation:
3x + 2y = 8
We can isolate y by subtracting 3x from both sides:
2y = 8 - 3x
Dividing both sides by 2, we get:
y = (8 - 3x) / 2
Now, we can substitute this expression for y into the second equation:
x - y = 1
Replacing y with (8 - 3x) / 2, we have:
x - (8 - 3x) / 2 = 1
To simplify this equation, we can multiply both sides by 2 to eliminate the fraction:
2x - (8 - 3x) = 2
Expanding the brackets, we get:
2x - 8 + 3x = 2
Combining like terms, we have:
5x - 8 = 2
Adding 8 to both sides:
5x = 10
Dividing both sides by 5:
x = 2
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the second equation:
x - y = 1
Replacing x with 2:
2 - y = 1
Subtracting 2 from both sides:
-y = -1
Multiplying both sides by -1:
y = 1
Therefore, the solution to the system of equations is x = 2 and y = 1, or (2, 1) as a coordinate point.