k well i had to use substitution to find the point of intersection for these 2 equations
x-y=10
3x+y=11
i chose to substitute y in the first equation
my final answer was (-1/2 , 5) can someone clarify this, and if it's wrong, where'd i make a mistake?
In the first equation, y= x-10
put that into the second to get
3x + x-10=11
4x=21
x= 4.25
Then you can solve for y.
It's right! Congrats!
Great job on using the substitution method to find the point of intersection between the two equations!
To clarify the steps you took, you correctly substituted the value of y from the first equation into the second equation. By substituting y = x - 10 into the second equation, you obtained:
3x + (x - 10) = 11
Next, you simplified the equation by combining like terms:
4x - 10 = 11
Then, you added 10 to both sides of the equation to isolate the 4x term:
4x = 21
To find the value of x, you divided both sides of the equation by 4:
x = 21/4 = 5.25
Now that you have the value of x, you can substitute it back into either of the original equations to solve for y. In this case, let's use the first equation:
x - y = 10
Since x = 5.25, you can substitute this value into the equation:
5.25 - y = 10
To solve for y, you subtract 5.25 from both sides of the equation:
- y = 10 - 5.25 = 4.75
To isolate y, you multiply both sides of the equation by -1:
y = -4.75
Therefore, the solution to the system of equations is (5.25, -4.75).
However, if you made an error in your calculations and obtained (-1/2, 5) instead, then there might have been a mistake during the calculations. You could review each step again to check if an error occurred during simplification or algebraic manipulations.