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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Gerhard

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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.

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) .

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

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