Question

find the point of intersection of 2x+y=3 and -x+2y=-4

Answer 1

To find the point of intersection of the two lines, we can solve the system of equations:

1) 2x + y = 3
2) -x + 2y = -4

First, we can solve equation 1 for y:
y = 3 - 2x

Then, substitute this expression for y into equation 2:
-x + 2(3 - 2x) = -4
-x + 6 - 4x = -4
6 - 5x = -4
-5x = -10
x = 2

Now, we can plug x = 2 back into either equation 1 or 2 to solve for y. Using equation 1:
2(2) + y = 3
4 + y = 3
y = -1

Therefore, the point of intersection of the two lines is (2, -1).