Question

5х + y = 16
х+ 6у = 38

Answer 1

Answer:

$(2,6)$

Step-by-step 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:

$\frac{-29y}{-29}=\frac{-174}{-29} \\\\y=6$

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:

$\frac{5x}{5}=\frac{10}{5}\\\\ x=2$

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

:Done