Solving with Elimination Practice
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Question
Solve the system of equations.
6x–5y=27
3x+5y=36
(1 point)
1. ( 7, 3)
2. ( -4, 2)
3. ( -1, -6)
4. ( 5, 3)
5. ( -1, 4)
To solve this system of equations, we can use the method of elimination. We will add the two equations together in a way that eliminates one of the variables.
Adding the two equations, we get:
(6x - 5y) + (3x + 5y) = 27 + 36
Combining like terms, we have:
9x = 63
Dividing both sides of the equation by 9, we find:
x = 7
Now, substitute the value of x into one of the original equations. Let's use the first equation:
6x - 5y = 27
6(7) - 5y = 27
42 - 5y = 27
Subtracting 42 from both sides:
-5y = -15
Dividing both sides by -5, we have:
y = 3
Therefore, the solution to the system of equations is x = 7 and y = 3.
To solve this system of equations using the elimination method, you need to add the two equations together to eliminate the y variable.
Let's start by adding the two equations:
(6x - 5y) + (3x + 5y) = 27 + 36
Simplifying the equation:
6x - 5y + 3x + 5y = 63
Combining like terms:
9x = 63
To isolate the x variable, divide both sides by 9:
9x/9 = 63/9
Simplifying:
x = 7
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:
6x - 5y = 27
Substituting x = 7:
6(7) - 5y = 27
Simplifying:
42 - 5y = 27
To isolate the y variable, subtract 42 from both sides:
42 - 42 - 5y = 27 - 42
Simplifying:
-5y = -15
To solve for y, divide both sides by -5:
-5y / -5 = -15 / -5
Simplifying:
y = 3
Therefore, the solution to the system of equations is x = 7 and y = 3.
To solve the system of equations using the elimination method, you need to eliminate one variable (either x or y) by adding or subtracting the equations. Let's solve this system of equations step by step.
Equation 1: 6x - 5y = 27
Equation 2: 3x + 5y = 36
To eliminate the variable "y," we will add the equations together.
(6x - 5y) + (3x + 5y) = 27 + 36
Simplifying the equation gives us:
9x = 63
Now, we can solve for x by dividing both sides of the equation by 9:
9x/9 = 63/9
x = 7
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use Equation 1:
6(7) - 5y = 27
Simplifying the equation gives us:
42 - 5y = 27
To isolate the variable "y," we subtract 42 from both sides:
-5y = 27 - 42
-5y = -15
Dividing both sides by -5, we get:
y = -15 / -5
y = 3
Therefore, the solution to the system of equations is x = 7 and y = 3.