Which is the best first step and explanation for solving the system of equations?
3x + 3y = 9
Add the second equation to the first equation.
4x + 2y = 4 and 2x + 4y = 14
Multiply both sides of each equation by 2.
-4x – 2y = -4 and x + 2y = 7
Multiply the first equation by -2.
(2x – x) + (y – 2y) = 2 – 7
Subtract the second equation from the first equation.
To solve the system of equations, the best first step is to subtract the second equation from the first equation.
Here’s why:
Given the two equations:
1) ( 4x + 2y = 4 )
2) ( 2x + 4y = 14 )
Subtracting the second equation from the first will allow you to eliminate one variable and solve for the other. This method is effective when the coefficients can easily lead to cancellation or simplification.
So the calculation is:
( (4x + 2y) – (2x + 4y) = 4 – 14 )
This simplifies to:
( 2x – 2y = -10 )
From here, you can further simplify or solve for ( x ) and ( y ).
Feel free to reach out if you need more detailed assistance on the next steps!
To solve the system of equations, the best first step is to subtract the second equation from the first equation.
Let’s look at your equations:
1. ( 4x + 2y = 4 )
2. ( 2x + 4y = 14 )
By subtracting the second equation from the first, you can eliminate one variable, making it easier to solve for the other.
So, subtracting the second equation from the first gives:
[(4x + 2y) – (2x + 4y) = 4 – 14]
[2x – 2y = -10]
This simplifies to:
[x – y = -5]
Now you can solve for one variable in terms of the other, which will lead you to the solution for both variables in the system.
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