Answer:
a) (2,9); b) no points of intersection
Explanation:
a)
Set the two equations equal to each other
7x - 5 = -2x + 13
Rearrange collecting like terms and solve
9x = 18
x = 2
Sub in x = 2 into either of the equations and it should yield the same result
Eq.1 y = 7(2) - 5 = 9
Eq.2 y = -2(2) + 13 = 9
Therefore the point of intersection is (2,9)
The graph confirms this result (see graph 1 with red and blue lines)
b)
As the gradients are the same, we can tell straight away that the two lines should be parallel and never intersect, but we'll try to solve it algebraically using the same method as in part a.
3x - 1 = 3x + 2
When rearranging, the x's cancel out which can be seen when subtracting 3x from both sides
-1 = 2
This equation is clearly incorrect. This means that there are no values of x at which the two equations are equal. Graphically, this means that the two lines are parallel and there are no points of intersection (see graph 2 with purple and green lines)