How do you solve this equation?

Question

4x+6y+2=0
9y=6x+21

Answer 1

4x + 6y + 2 =0     -(1)

6x - 9y + 21 =0    -(2)

Multiply the each side by first equation 6 and second equation 4

then the equations becomes

24x + 36y + 12 = 0    -(3)

24x - 36y + 84 = 0    -(4)

Subtract from third to fourth

72y - 72 = 0

Add 72 to each side

72y = 72

Divide each side  by 72

y = 1

Substitute y = 1 in the first equation

4x + 6(1) + 2 = 0

4x + 8 = 0

Subtract 8 from each side

4x = -8

Divide each side by 4

x = -2

Therefore the solutions of the equations : x = -2 , y = 1.

 

 

Answer 2

Elimination method :

The equations are 4x + 6y + 2 = 0 and 9y = 6x + 21 

Write the equations in standard form of a line equation, i.e, ax + by = c.

4x + 6y  = - 2 → ( 1 )

6x - 9y = - 21 → ( 2 )

Step1:

Multiply  equations by constants to get two equations that contain opposite terms.

4x + 6y = -2   multiply by 6  24x + 36y = -12

6x - 9y = -21  multiply by 4  24x - 36y = - 84

Step2:

Add the equations, to elimiinate one variable.

Step3:

Subtitute the value in any one of the equations to solve other variable.

Take the equation 4x + 6y  = - 2

4(-2) + 6y = -2

6y = - 2 + 8

y = 1

Solution x = -2 and y = 1.