Solve the system of equations: what is the y-value in the solution?
3x - 5y = -16 and 2x + 5y = 31
add them:
5x = 15
x = 3
sub into 2x+5y=31
6 + 5y = 31
5y = 25
y = 5
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one variable by adding or subtracting the equations to create a new equation with just one variable.
First, let's eliminate the variable "y". To do this, we can add the two equations together:
(3x - 5y) + (2x + 5y) = (-16) + 31
Simplifying the equation, we get:
5x = 15
To solve for "x", we divide both sides of the equation by 5:
x = 3
Now that we have the value of "x", we can substitute it back into one of the original equations to solve for "y". Let's substitute it into the second equation:
2(3) + 5y = 31
Simplifying the equation, we get:
6 + 5y = 31
Next, we solve for "y" by subtracting 6 from both sides of the equation:
5y = 25
Dividing both sides of the equation by 5, we find:
y = 5
So, the solution to the system of equations is x = 3 and y = 5. Therefore, the y-value in the solution is 5.