Answer:
The intersection point is (2, 3)
Step-by-step explanation:
The given (linear) equations for the point of intersection is required are;
y = x + 1...(1)
3·y + 2·x = 13...(2)
To find the point of intersection without using graph, we note that the point of intersection is the point at which the values of both equations are equal
We find the values of 'x' and y-coordinates at the point of intersection as follows;
Making 'y' the subject of equation (2) gives;
y = (13 - 2·x)/3
When both lines intersect, the 'x' and y-values are the same;
y = x + 1 for the first line, and y = (13 - 2·x)/3 for the second line, therefore, at the intersection point, we have;
y = y
x + 1 = (13 - 2·x)/3
3·(x + 1) = 13 - 2·x
3·x + 3 = 13 - 2·x
3·x + 2·x = 13 - 3
3·x + 2·x = 5·x = 13 - 3 = 10
∴ 5·x = 10
Therefore, at the point of intersection, x = 10/5 = 2
x = 2
'y' is given in equation (1) by y = x + 1, therefore, at the point of intersection, 'x = 2', we get;
y = x + 1
∴ The value of 'y' at the point of intersection is y = 2 + 1 = 3
y = 3
Therefore, the (x, y) coordinate at the point of intersection is (2, 3) which can be written as follows;
The point of intersection = (2, 3).