Given two lines 𝐿1: 𝑥 + 4𝑦 = −10 and 𝐿2: 2𝑥 − 𝑦 = 7. i. Find the intersection point of 𝐿1 and 𝐿2.

To find the intersection point of two lines, we need to solve the system of equations formed by the equations of the lines.

Given:
Line L1: x + 4y = -10
Line L2: 2x - y = 7

We can solve this system of equations by using any method like substitution, elimination, or matrices. Let's solve it using the substitution method.

Step 1: Solve one equation for one variable in terms of the other variable.
From the equation of L2, we can isolate y:
y = 2x - 7.

Step 2: Substitute the expression for the variable in the other equation.
Substitute y with (2x - 7) in the equation of L1:
x + 4(2x - 7) = -10.

Step 3: Simplify and solve for the remaining variable.
x + 8x - 28 = -10
9x - 28 = -10
9x = 18
x = 2.

Step 4: Substitute the value of x back into one of the original equations to find the value of y.
Using L2: 2(2) - y = 7
4 - y = 7
-y = 7 - 4
-y = 3
y = -3.

Therefore, the intersection point of L1 and L2 is (2, -3).

Answer: The intersection point of L1 and L2 is (2, -3).