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



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

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

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).

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