To solve the system of equations:
x - 5y = 15 (Equation 1)
4x - 3y = 26 (Equation 2)
There are several methods for solving a system of equations, but we will use the elimination method here. We will eliminate one variable by adding or subtracting the two equations.
Multiplying Equation 1 by 4, we get:
4x - 20y = 60 (Equation 3)
Now we can subtract Equation 2 from Equation 3:
(4x - 20y) - (4x - 3y) = 60 - 26
Simplifying, we get:
-17y = 34
Dividing both sides by -17, we get:
y = -2
Substituting this value of y in Equation 1, we get:
x - 5(-2) = 15
Simplifying, we get:
x + 10 = 15
Subtracting 10 from both sides, we get:
x = 5
Therefore, the solution to the system of equations is:
x = 5 and y = -2
In other words, the two equations intersect at the point (5, -2).