Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin?
the system: 2x+y=-3 3x-2y=2
To solve the system by elimination, you need to eliminate one variable by manipulating the equations. Here's one possible way to begin:
1. Multiply the first equation by 2 to make the coefficients of y in both equations equal:
2 * (2x + y = -3) = 4x + 2y = -6
2. Now, add this modified equation to the second equation:
(4x + 2y) + (3x - 2y) = -6 + 2
Simplifying, you get:
7x = -4
This step helps in eliminating the y variable.
To solve the system of equations by elimination, the goal is to eliminate one of the variables by manipulating the equations. In this case, the best way to begin is to choose a variable to eliminate by multiplying one or both of the equations by a scalar (a number) to make the coefficients of one of the variables equal in magnitude but opposite in sign.
To eliminate the variable "y" in this system, we can multiply the first equation by 2 and the second equation by 1:
Step 1: Multiply the first equation by 2 and the second equation by 1.
2(2x + y) = 2(-3)
3x - 2y = 2
This results in the following modified system:
4x + 2y = -6
3x - 2y = 2
Now, the coefficients of "y" are equal but opposite in sign, allowing us to eliminate the "y" variable in the next step.
To solve the system of equations by elimination, we need to eliminate one of the variables by manipulating the given equations. Here are the steps to begin:
1. Choose a variable to eliminate: In this case, it would be convenient to eliminate either 'x' or 'y' by adding or subtracting the equations. Let's choose to eliminate the 'y' variable.
2. Multiply the equations: We need to manipulate one or both of the equations so that the coefficients of 'y' in both equations are the same (or differ by a multiple of each other).
Looking at the coefficients of 'y' in the given equations, we could multiply the first equation by 2, which will result in 4x+2y=-6. Now the coefficients of 'y' in both equations are the same (2).
3. Add the equations: Add the manipulated equations together to eliminate the 'y' variable. In this case, adding the two equations gives us:
(4x + 2y) + (3x - 2y) = -6 + 2.
Simplifying the equation, we get:
7x = -4.
So, the first step to begin solving the given system of equations by elimination is to multiply the first equation by 2.