Elimination ( show work please)
6x+5y=39
3x+5y=27
subtract second equation from first.
3x=12 solve for x.
to elminiate x, multiply second equation by 2
6x+5y=39
6x+10y=54
now subtract second equation from first.
-5y=-15 solve for y
To solve this system of equations using the elimination method, we want to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable "y" by subtracting the second equation from the first equation.
Let's start by subtracting the second equation from the first equation:
(6x + 5y) - (3x + 5y) = 39 - 27
Simplifying the equation, we get:
6x - 3x + 5y - 5y = 12
Combining like terms, we have:
3x = 12
Now divide both sides of the equation by 3 to solve for x:
3x/3 = 12/3
x = 4
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y.
Let's substitute x = 4 into the first equation:
6(4) + 5y = 39
24 + 5y = 39
Next, subtract 24 from both sides of the equation:
5y = 39 - 24
5y = 15
Finally, divide both sides of the equation by 5 to solve for y:
5y/5 = 15/5
y = 3
Therefore, the solution to the system of equations is x = 4 and y = 3.
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, we can eliminate the "y" variable by subtracting the second equation from the first equation.
1. Multiply the second equation by -2 to make the y-coefficients in both equations equal:
(-2) * (3x + 5y) = (-2) * 27
-6x - 10y = -54
2. Now, add the modified second equation to the first equation:
(6x + 5y) + (-6x - 10y) = 39 + (-54)
(6x - 6x) + (5y - 10y) = -15
Simplifying the equation:
-5y = -15
3. Divide both sides of the equation by -5 to solve for "y":
y = -15 / -5
y = 3
Now that we have the value of "y," we can substitute it back into one of the original equations (let's use the first equation) to find the value of "x":
6x + 5(3) = 39
6x + 15 = 39
4. Subtract 15 from both sides:
6x = 39 - 15
6x = 24
5. Divide both sides by 6 to solve for "x":
x = 24 / 6
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 3.