anonymous
  • anonymous
Which system has (-2, -2) as the solution? Which system has no solutions? Which system has infinite solutions? A. x + y = -1 4x + 4y = -4 B. x + y = -4 -3x + 2y = 2 C. 4x + 6y = -12 2x + 3y = 9 D. x - y = -2 3x - y = 0 E. x - 4y = -8 2x - 3y = -16
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
A) x +y =-1 4x + 4y = -4 The second equation is just 4 times the first equation. So there are inifinty solutions. i.e multiply the first by 4 => 4x +4y =-4 ( first equation) 4x + 4y =-4 you cannot isolate a single variable either x or y B) x + y = -4 -3x + 2y = 2 Multiply the first equation by 3 and add both equation to eliminate x and solve for y: i.e. 3x + 3y = -12 -3x + 2y = 2 ----------------- => 5y = -10 y = -2 substitute the value of y back into any one of the original equations to solve for y e.g. substitute into x +y = -4 => x -2 = -4 add 2 on both sides => x = -2 Hence the solution is ( -2, -2) C) C. 4x + 6y = -12 2x + 3y = 9 The left hand side of the equations are multiples of each other. e.g Multiply the second equation by 2 yields: 3x + 6y = 18 i.e the system becomes: 4x + 6y = -12 4x + 6y = 18 This system has no solution for example subtract the second from the first yields: 0 + 0 = -30 D.x - y = -2 3x - y = 0 Reqwrite the system as: -3x +3y = -6 ( after multiplying the first equation by -3 ) 3x -y = 0 Add the two to yied 2y = 6 y = 3 D has a solution (1, 3) E.x - 4y = -8 2x - 3y = -16 Multiply the first equation by -2 -2x +8y = 16 2x -3y = -16 Add the two equations: 5y = 0 y =0 => x = -8 ( by plugging the value of y=0 in any one of the original equations) E has solution: ( -8,0)
anonymous
  • anonymous
Therefore: A has ininifinity solutions B has solution ( -2, -2) C has no solution

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