julia was asked to solve the system of equations below by elimination. which of the following would be the best way to begin
i. 2x + y = -3
ii. 3x - 2y = 2
The best way to begin solving the system of equations by elimination would be to multiply the first equation by a constant so that the coefficients of y in both equations are equal. This way, when the equations are added together, the y terms will cancel out. In this case, it would be best to multiply equation i by 2.
i. 2(2x + y) = 2(-3)
4x + 2y = -6
ii. 3x - 2y = 2
Now, you can add equation ii to the modified equation i to eliminate y.
To solve the given system of equations by elimination, the best way to begin is to eliminate one variable by adding or subtracting the equations.
In this case, the coefficients of the y term in both equations are already the same, so it would be easier to eliminate y by adding the equations.
So, the best way to begin is to add the two equations together:
(i) 2x + y = -3
(ii) 3x - 2y = 2
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(i) + (ii) becomes: 5x - y = -1
Therefore, the best way to begin is to add the two equations together, resulting in the equation 5x - y = -1.
To solve the system of equations using the elimination method, you need to eliminate one variable by multiplying one or both equations by a suitable constant.
Looking at the given system of equations:
i. 2x + y = -3
ii. 3x - 2y = 2
In this case, it would be best to first eliminate the variable "y" by multiplying equation i by 2 or multiplying equation ii by -1.
Let's choose to multiply equation i by 2 to eliminate the variable "y".
By multiplying equation i by 2, the system of equations becomes:
iii. 4x + 2y = -6
ii. 3x - 2y = 2
Now, adding equations iii and ii eliminates the variable "y":
(4x + 2y) + (3x - 2y) = -6 + 2
Simplifying the equation:
4x + 2y + 3x - 2y = -4
Combining like terms, you get:
7x + 0y = -4
The variable "y" has been eliminated, leaving only "x" in the equation. This allows us to solve for "x" easily.
So, the best way to begin solving the given system of equations by elimination is to multiply equation i by 2.