Solve the following pair of equations: $6x+5y=7x+3y+1=2x+12y-2$
- $x=3, \, y=2$
- $x=1, \, y=0$
- $x=5, \, y=3$
- $x=7, \, y=1$
Reveal answer
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A
Correct answer
Explanation
6x + 5y = 7x + 3y + 1 => x - 2y = -1. 7x + 3y + 1 = 2x + 12y - 2 => 5x - 9y = -3. From first, x = 2y - 1. Substitute: 5(2y - 1) - 9y = -3 => 10y - 5 - 9y = -3 => y = 2. Then x = 2(2) - 1 = 3.
AI explanation
Split the equality into two equations: 6x + 5y = 7x + 3y + 1 and 7x + 3y + 1 = 2x + 12y - 2. The first equation simplifies to x - 2y = -1, and the second simplifies to 5x - 9y = -3. Multiplying the first simplified equation by 5 gives 5x - 10y = -5. Subtracting this from the second simplified equation yields y = 2. Substituting y = 2 into x - 2y = -1 gives x = 3.