Solve the following system of equations by either substitution or linear combination...?

Question

Solve the following system of equations by either substitution or linear combination...

2x - 3y = 1
4y + 3x = 27

Answer 1

2x - 3y = 1 ---- (1)
4y + 3x = 27 ---- (2)

from (1):
x= (3y+1)/2 ---- (3)

Subst (3) into (2)
4y + 3[(3y+1)/2 ] = 27
8y + 9y + 3 = 54
17y = 51
y = 3
x = 5

Answer 2

choose one equation and move everything accordingly to get a single variable by itself (x or y) on one side of the equal sign....then plug it back in to the second equation..

2x - 3y = 1 >>>>>>>> (1+3y)/2 = x

4y + 3 [(1+3y)/2] = 27 solve for y....then plug that back in to either equation to get the value of x..

Answer 3

x=1+3y/2

4y + 3 (1+3y/2)=27

4y+3+9y/2=27

(8y+3+9y)/2=27

(17y+3)=27*2

17y+3=54

17y=51

y=3


x=5

Answer 4

-3 * (2x - 3y = 1)
2 * (4y + 3x = 27)
---------------------------
-6x + 9y = -3
8y + 6x = 54
-------------------------
17y = 51
Therefore: y = 3

Using one of the previous equations:
2x - 3y = 1
We know y = 3
Therefore:
2x - 3(3) = 1
2x - 9 = 1
2x = 10
x = 5

Check:
2(5) - 3(3) = 1
10 - 9 = 1
1 = 1

Answer 5

8x - 12y = 4
9x + 12y = 81----ADD
17x = 85
x = 5
4y + 15 = 27
4y = 12
y = 3

x = 5 , y = 3