Question

5х + y = 16
х+ 6у = 38

Answer 1

`(2,6)`

Explanation:

Solve by substitution. Solve the second equation for x:

`x+6y=38\\\\x+6y-6y=38-6y\\\\x=38-6y`

Insert the value of x into the first equation:

`5(38-6y)+y=16`

Solve for y. Simplify multiplication using the distributive property:

`5(38)+5(-6y)+y=16\\\\190-30y+y=16\\\\190-29y=16`

Subtract 190 from both sides:

`190-190-29y=16-190\\\\-29y=-174`

Isolate the variable to find its value. Divide both sides by -29:

`(-29y)/(-29)=(-174)/(-29) \\\\y=6`

Now take the value of y and insert back into either equation to solve for x:

`5x+6=16`

Subtract 6 from both sides:

`5x+6-6=16-6\\\\5x=10`

Divide both sides by 5:

`(5x)/(5)=(10)/(5)\\\\ x=2`

Therefore, the solution to the system is
`(2,6)`.

:Done