Solve the following system of equations using elimination Be

Solve the following system of equations using elimination. Be sure to provide an in-between step and conclude how many solutions there are to the system. If there is only one solution, write that solution as an ordered pair 5x + y = 2 and 3x + 2y = 11

Solution

5x + y = 2 and 3x + 2y = 11

let 5x + y = 2 be equation 1

and 3x + 2y = 11 be equation 2

now multiply equation 1 with number 2 and subtract it from equation2

2(5x +y=2)

10x +2y =4

3x +2y   =11

-    -        -

after subtracting

7x = 4-11

7x = -7

so x=-1

and

plug x=1 in equation 2

3(-1) +2y =11

-3 +2y =11

2y= 14

y =7

only one solutio is present

that solution is (-1 ,7)