Solve the following system using the elimination method:
10x - 6y = -16
5x + 2y = 22
Add three times the second equation to the first to get:
(10+15)x=-16+66
25x = 50
x=2
Substitute x=2 into the second equation to get:
5(2)+2y=22
2y=22-10=12
y=6
Now substitute x=2 and y=6 into the first equation to check solution
10(2)-6(6)=-16 so solution is correct.
To solve the system using the elimination method, you need to eliminate one of the variables by adding or subtracting the equations. The goal is to create a new equation with just one variable so that you can solve for it.
Let's begin by eliminating the variable "y". In order to do that, we need to make the coefficients of "y" in both equations the same (except one will be positive and the other negative).
Multiply the second equation by 3, so that the coefficient of "y" becomes -6 in both equations:
3 * (5x + 2y) = 3 * 22
15x + 6y = 66
Now, your system of equations becomes:
10x - 6y = -16
15x + 6y = 66
Now, add the two equations together to eliminate "y":
(10x - 6y) + (15x + 6y) = -16 + 66
25x = 50
Next, divide both sides of the equation by 25 to solve for "x":
25x/25 = 50/25
x = 2
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
10x - 6y = -16
Substitute x = 2:
10(2) - 6y = -16
20 - 6y = -16
Now, solve for "y":
-6y = -16 - 20
-6y = -36
y = -36 / -6
y = 6
Therefore, the solution to the system of equations is x = 2 and y = 6.
To solve the system using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations together. Let's start by eliminating the y variable.
First, we can multiply the second equation by 3 to make the coefficient of y in both equations the same (6y and -6y):
3*(5x + 2y) = 3*(22)
15x + 6y = 66
Now, we will add the two equations together:
(10x - 6y) + (15x + 6y) = -16 + 66
10x + 15x - 6y + 6y = 50
25x = 50
Next, we will solve for x by dividing both sides of the equation by 25:
25x/25 = 50/25
x = 2
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 use the first equation:
10x - 6y = -16
10(2) - 6y = -16
20 - 6y = -16
Next, we will solve for y by subtracting 20 from both sides of the equation:
-6y = -16 - 20
-6y = -36
Then, divide both sides by -6 to get the value of y:
-6y/-6 = -36/-6
y = 6
So, the solution to the system is x = 2 and y = 6.