Solve the simultaneous equations x + y = 2 and 3x - 2y = 1
Answer Details
To solve the simultaneous equations x + y = 2 and 3x - 2y = 1, we can use the method of substitution or elimination.
Method of Substitution:
We can solve for one variable in terms of the other from the first equation and substitute it into the second equation, then solve for the other variable. Let's solve for y in terms of x from the first equation:
x + y = 2
y = 2 - x
Now substitute y = 2 - x into the second equation:
3x - 2y = 1
3x - 2(2 - x) = 1
3x - 4 + 2x = 1
5x = 5
x = 1
Now substitute x = 1 into either equation to find y:
x + y = 2
1 + y = 2
y = 1
Therefore, the solution is x = 1 and y = 1.
So, the correct answer is: x = 1 and y = 1.