Final answer:
To find the coordinates of the intersection of the given equations, substitute the second equation into the first, solve for x, and then find y. The coordinates of the intersection point are (-4, 5).
Step-by-step explanation:
The student is asking how to find the coordinates of the intersection point of two linear equations: 4x+7y=19 and y=x+9. To solve this system of equations, we can use substitution. Since the second equation gives us y in terms of x, we can substitute y in the first equation with x+9:
4x + 7(x + 9) = 19
Simplifying this we get:
4x + 7x + 63 = 19
11x + 63 = 19
11x = -44
x = -4
Now, we substitute x back into the second equation to find y:
y = (-4) + 9
y = 5
Therefore, the coordinates of the intersection point are (-4, 5).