Find the equation of the line that passed through the point of intersection of 4x + y = -13, 3x - 4y = 14 and is parallel to the line 5x + 3y - 4 = 0.

3y + 5x + 25 = 0

Step-by-step explanation:

Step 1: Find the coordinates of intersection of the two lines by solving the two equations.

4x + y = -13

3x - 4y = 14

Step 2: To eliminate y, make the coefficient equal, add if the variable have the different sign and subtract if the have the same sign.

4x + y = -13   ---(1)  x 4

3x - 4y = 14   ---(2)  x 1

16x + 4y = -52

3x - 4y = 14

19x = -38

x = -38/19 = -2

Step 3: Substitute x = -2 to find y.

3x - 4y = 14

3(-2) - 4y = 14

-6 - 4y = 14

-4y = 14 + 6

-4y = 20

Step 4:

Therefore, the point of intersection is (x,y) = (-2,-5)

Hence the line passes through the point (-2, -5)

Step 6: since the line that passes through (-2, -5) is parallel to 5x + 3y - 4 = 0, the slope will the equal to the slope of 5x + 3y - 4 = 0

For parallel lines

m1 = m2

5x + 3y - 4 = 0

3y = -5x + 4

m1 = -5/3

m2 = -5/3