Answer:
1A. (2, 4)
1B. (2, 4)
2. All three lines would intersect at the point (2, 4).
3. The solution to both of those equations is (2, 4). We know this because we already know they both equal y=2+x. If a=b and a=c, then b=c.
4.
line 1: y = 1 + x
line 2: y = 4x - 2
line 3: 2x + y = 4 or y = -2x +4
Explanation:
1A.
y = 2 + x
y = 3x -2
because both equations equal y, set them equal to each other
2 + x = 3x - 2
solve for x by moving x to one side, and constants to the other
2 = 2x - 2 (subtract x from both sides)
4 = 2x (add 2 to both sides)
2 = x (divide both sides by 2)
this gives the x coordinate of 2 (2, y)
solve for y by substituting the x coordinate into one of the original equations
y = 2 + 2
y = 4
this gives the y coordinate, making the complete answer (2, 4)
1B.
y = 2 + x
2x + y = 8
first, solve the second equation for y
2x + y = 8 (subtract the x variable from both sides
y = 8 - 2x (arrange properly)
y = -2x + 8
second, set the now equal equations equal to each other
2 + x = -2x + 8
now, solve for x
2 + 3x = 8 (add the x variable - 2x - to both sides)
3x = 6 (subtract the constant - 2 - from both sides)
x = 2 (divide both sides by the constant connected to x)
this gives the x coordinate of 2 (2, y)
solve for y by substituting the x coordinate into one of the original equations
y = 2 + 2
y = 4
this gives the y coordinate, making the complete answer (2, 4)
sorry it took so long, i do hope this helps, have a lovely day <3