Solve the system by substitution 4x+4y = 12 and x+2y=11

4x+4y=12

x+2y=11

is there a solution?

x = - 5 and y = 8

Step-by-step explanation:

To solve the system by substitution, solve one equation for a variable. Then substitute the equation into the other equation.

x + 2y = 11 becomes x = 11 - 2y

Substitute x = 11 - 2y into 4x + 4y = 12.

4 (11-2y) + 4y = 12

44 - 8y + 4y = 12

44 - 4y = 12

32 = 4y

y = 8

Substitute again with y = 8 into the equation to find x.

x = 11 - 2 (8)

x = 11 - 16

x = - 5