Solve the system of equations using with multiplication
4x-6y=-48
-2x+4y=30
To solve the system of equations using multiplication, we can multiply both equations by a constant to eliminate a variable.
Let's start with the second equation:
-2x + 4y = 30
If we multiply this equation by 2, we can eliminate x:
(2)(-2x + 4y) = (2)(30)
-4x + 8y = 60
Now we have:
4x - 6y = -48
-4x + 8y = 60
Adding these two equations together:
(4x - 6y) + (-4x + 8y) = -48 + 60
2y = 12
y = 6
Now, we can substitute this value of y back into one of the original equations to solve for x. Let's use the first equation:
4x - 6(6) = -48
4x - 36 = -48
4x = -48 + 36
4x = -12
x = -12/4
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 6.
To solve the system of equations using multiplication, we need to eliminate one variable by multiplying one or both equations.
Let's start by eliminating the variable "x" by multiplying the second equation by 2. This will make the coefficients of "x" in both equations equal:
2(-2x + 4y) = 2(30)
-4x + 8y = 60
Now, rewrite the system of equations:
4x - 6y = -48
-4x + 8y = 60
Next, add the two equations together to eliminate the "x" variable:
(4x - 6y) + (-4x + 8y) = -48 + 60
-6y + 8y = 12
2y = 12
Now, divide both sides of the equation by 2 to solve for "y":
2y/2 = 12/2
y = 6
We have found the value of "y" to be 6.
Next, substitute this value back into one of the original equations to solve for "x". Let's use the first equation:
4x - 6(6) = -48
4x - 36 = -48
Add 36 to both sides of the equation:
4x - 36 + 36 = -48 + 36
4x = -12
Finally, divide both sides of the equation by 4 to solve for "x":
4x/4 = -12/4
x = -3
The solution to the system of equations is x = -3 and y = 6.
To solve the system of equations using multiplication, we will first eliminate one of the variables (either x or y) using multiplication, and then solve for the remaining variable.
Let's start by eliminating the variable x. We will multiply both sides of the second equation by 2 to make the coefficients of x in both equations the same:
-2x + 4y = 30 (multiply all terms by 2)
-4x + 8y = 60
Now, we have the following system of equations:
4x - 6y = -48
-4x + 8y = 60
Next, we will add the two equations together to eliminate the variable x:
(4x - 6y) + (-4x + 8y) = -48 + 60
The x terms will cancel out:
4x - 4x - 6y + 8y = 12
Simplifying the equation:
2y = 12
Now, we can solve for y by dividing both sides of the equation by 2:
2y / 2 = 12 / 2
y = 6
We have found the value of y. Now, we can substitute this value back into one of the original equations to solve for x. Let's use the first equation:
4x - 6y = -48
Plugging in y = 6:
4x - 6(6) = -48
4x - 36 = -48
Now, we will solve for x:
4x = -48 + 36
4x = -12
Dividing both sides by 4:
4x / 4 = -12 / 4
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 6.