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

well there are two answers for that.

1: you need 120 ones then that will equal up to 120.

2: you could also do one 100 and 2 tens.

those are the answers that i have thought of.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1