Question

Please Help!!!!!!


Solve the equations for the solutions, x and y .

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

The lines intersect at __, __

Answer 1

Let's use the substitution method. We'll solve for x in the second equation, then substitute it back in the first equation to solve for y, finally substituting that y value in for x.

x -2y = -1
x -2y +2y = -1 +2y
x = 2y -1

Great, now we have x. Let's put it into the first equation.

2x +y = 3
2(2y -1) +y = 3
4y -2 +y = 3
5y -2 = 3
5y -2 +2 = 3 +2
5y = 5
5y/5 = 5/5
y = 1

There's your y value. Now, we already know that x = 2y -1. Let's plug y in there to get x.

x = 2y -1
x = 2(1) -1
x = 2 -1
x = 1

There's x. Now, plug y = 1 and x = 1 into a coordinate pair, and you have your intersection point.