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If the equation 2x+3y+1=0,3x+y-2=0,and ...

If the equation `2x+3y+1=0,3x+y-2=0,and ax+2y-b=0` are consistent, then prove that `a-b=2.`

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To prove that \( a - b = 2 \) given that the equations \( 2x + 3y + 1 = 0 \), \( 3x + y - 2 = 0 \), and \( ax + 2y - b = 0 \) are consistent, we will follow these steps: ### Step 1: Rewrite the equations We have the following equations: 1. \( 2x + 3y + 1 = 0 \) (Equation 1) 2. \( 3x + y - 2 = 0 \) (Equation 2) 3. \( ax + 2y - b = 0 \) (Equation 3) ...
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