5x+y=16
x-2y=1
i dont knw
5x+y=16
x-2y=1
x = 1 + 2y
5 (2y + 1) + y = 16
10y + 5 + y = 16
11y = 11
y = 1
x - 2 = 1
x = 3
To solve this system of linear equations, we can use either the substitution method or the elimination method. I will show you how to solve it using the substitution method.
The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation.
Let's solve the second equation for x:
x - 2y = 1
Add 2y to both sides of the equation:
x = 2y + 1
Now substitute this expression for x in the first equation:
5(2y + 1) + y = 16
Distribute 5 to both terms inside the parentheses:
10y + 5 + y = 16
Combine like terms:
11y + 5 = 16
Now, let's isolate y by subtracting 5 from both sides:
11y = 16 - 5
11y = 11
Divide both sides by 11:
y = 1
Now that we have the value of y, substitute it back into one of the original equations to solve for x. Let's use the first equation:
5x + y = 16
Substitute y = 1:
5x + 1 = 16
Subtract 1 from both sides:
5x = 16 - 1
5x = 15
Divide by 5:
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.