## Solve the system of equations. ​ −5x−3y−9=0 4x−18y−54=0 y=? x=? ​

Question

Solve the system of equations.

−5x−3y−9=0
4x−18y−54=0
y=? x=?

in progress 0
2 months 2021-07-30T02:06:28+00:00 1 Answers 2 views 0

Step-by-step explanation:

Eq. 1 )   −5x−3y−9=0

Eq. 2)   4x−18y−54=0

there are two routes to solve this,   Substitution or  elimination,  I’ll go for the 2nd one because I can see that the y values are a multiple of each other 🙂

6 *( −5x−3y−9=0 )

Eq. 3) -30x -18y =54

subtract Eq. 2 from Eq. 3  🙂

-30x -18y =54

-( 4x−18y=54)

-34x = 0

so according to the equations then x =0 but,  that’s not really a full answer, so now we should go back and try the other method, substitution,

then:

-5x = 9 +3y

x = – 9/5 + (-3/5)y

now plug that into Eq. 2

4( – 9/5 + (-3/5)y ) – 18y = 54

-36/5 + (-12/5)y -18y = 54

(-12/5)y – (90/5)y = 54+36/5

-(102/5)*y =270/5+36/5

-(102/5)y = 306/5

y = (-5/102)*(306/5)

y = -306/102

y = -3

then plug in for either equation

-5x-3( -3) = 9

-5x + 9 = 9

-5x = 0

x = 0

now we have the full answer

check it by plugging in both x and y into the 2nd equation

4(0) – 18(-3) = 54

54= 54

this seems good