To solve the system of equations using the elimination method, the goal is to eliminate one of the variables by manipulating the equations. Given the system:
- \( 2x + y = -3 \) (i)
- \( 3x - 2y = 2 \) (ii)
A good first step would be to align the coefficients of \( y \) or \( x \) to eliminate one of the variables. In this case, let's eliminate \( y \) because one equation already has \( y \) with a coefficient of 1 and the other has a coefficient of -2.
To do this, we can multiply the first equation by 2, so the coefficient of \( y \) in the first equation matches the coefficient of \( y \) in the second equation (but with opposite sign):
Multiply equation (i) by 2: \[ 4x + 2y = -6 \quad \text{(iii)} \]
Now we have the following system:
- \( 4x + 2y = -6 \) (iii)
- \( 3x - 2y = 2 \) (ii)
Next, we can add these two equations to eliminate \( y \): \[ (4x + 2y) + (3x - 2y) = -6 + 2 \] This gives: \[ 7x = -4 \]
Thus, the best way for Julie to begin solving this system by elimination is to multiply the first equation \( 2x + y = -3 \) by 2 to prepare for elimination of \( y \).
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