solve the systems of equations
x +2y=6
3x-2y=-22
is the answer y=-48 or is it y=5
take the first eq. and solve for x. (x=6-2y). plug into second eq. and solve for y. you should be able to figure it out
Adding the two equations
gives
4x=28,
and solve for x
To solve the given system of equations:
1. Start by adding the two equations together to eliminate the y-term.
(x + 2y) + (3x - 2y) = 6 + (-22)
4x = -16
x = -16/4
x = -4
2. Substitute the value of x (-4) into one of the original equations to solve for y.
x + 2y = 6
-4 + 2y = 6
2y = 6 + 4
2y = 10
y = 10/2
y = 5
Therefore, the solution to the system of equations is x = -4 and y = 5. So, y = 5 is the correct answer.
To solve the system of equations:
1) We will use the method of elimination to eliminate one of the variables. Let's begin by multiplying the first equation by 3 and the second equation by 1, this way, when we add them together the y terms will cancel out.
(3)(x + 2y) = (3)(6) --> 3x + 6y = 18
(1)(3x - 2y) = (1)(-22) --> 3x - 2y = -22
2) Now, we will add the two equations together to eliminate the y terms:
(3x + 6y) + (3x - 2y) = 18 + (-22)
3x + 3x + 6y - 2y = -4
6x + 4y = -4
3) Simplify the equation:
6x + 4y = -4
4) To isolate a variable, let's express x in terms of y:
6x = -4 - 4y
6x = -4y - 4
x = (-4y - 4)/6
x = (-2y - 2)/3
5) Now that we have the expressions for x and y, we can substitute either of them into one of the original equations to find the value of the other variable.
Given the original equation: x + 2y = 6
Substituting x = (-2y - 2)/3 into the equation:
(-2y - 2)/3 + 2y = 6
-2y - 2 + 6y = 18
4y - 2 = 18
4y = 20
y = 20/4
y = 5
6) Now that we have the value of y, substitute it back into either equation to find the value of x:
x + 2(5) = 6
x + 10 = 6
x = 6 - 10
x = -4
Therefore, the solution to the system of equations is x = -4 and y = 5.
The answer is y = 5, not y = -48.