Solve the following systems by solving one of the equations

Solve the following systems by solving one of the equations for x or y and then using the substitution method. x + 3y = 4 x - 2y = -1 x - y = 5 x + 2y = -1 2x + y = 1 x - 5y = 17 2x - 2y = 2 x - 3y = -7 3x + 5y = -3 x - 5y = -5 2x - 4y = -4 x + 2y = 8 5x + 3y = 0 x - 3y = -18 x - 3y = -5 x - 2y = 0 -3x - 9y = 7 x + 3y = 12 2x + 6y = -18 x + 3y = -9 Solve the following systems using the substitution method. 5x - 8y = 7 y = 2x - 5 3x + 4y = 10 y = 8x - 15

Solution

13) x+3y = 4 ----(1)

x -2y = -1 ----(2)

x +3y =4

x= -1 +2y

-1 +2y +3y =4 ----> 5y = 5 ; y =1

x +3*1 = 4 ---> x =1

(x, y) = ( 1, 1)

14 ) x - y = 5 ----(1)

     x+2y = -1 ----(2)

from equation x= 5+y

5+y +2y =-1 ; 3y = -6 ; y = -2

x= 5+y = 5 -2 =3

(x, y) ---> ( 3, -2)

15) 2x +y =1 ----(1)

x - 2y = -1 -----(2)

from equation : x= -1 +2y

2(-1+2y) +y =1

-2 +4y +y =1 ; 5y = 3

y = 3/5

x= -1+2*3/5 = 1/5

(x, y) ---( 1/5 , 3/5)

16) 2x - 2y = 2 ----(1)

x - 3y = -7 ----(2)

from equation 2 : x= -7 +3y

substitute in equation (1) : 2(-7 +3y) - 2y =2

-14 +6y -2y = 2

4y = 16 ;y =4

x = -7 +3*4 = 5

Solution (x, y) = (5, 4)