Which system has no solution?Responsesy=9x+6.25−18x+2y=12.5y is equal to 9 x plus 6 point 2 5; negative 18 x plus 2 y is equal to 12 point 5y=3x+9x+8y=12.3y is equal to 3 x plus 9; x plus 8 y is equal to 12 point 3y=4.5x−5−3x+2y=6y is equal to 4 point 5 x minus 5; negative 3 x plus 2 y is equal to 6y=−3x+86x+2y=−4.5
Question
Which system has no solution?Responsesy=9x+6.25−18x+2y=12.5y is equal to 9 x plus 6 point 2 5; negative 18 x plus 2 y is equal to 12 point 5y=3x+9x+8y=12.3y is equal to 3 x plus 9; x plus 8 y is equal to 12 point 3y=4.5x−5−3x+2y=6y is equal to 4 point 5 x minus 5; negative 3 x plus 2 y is equal to 6y=−3x+86x+2y=−4.5
Solution
To determine which system has no solution, we need to put each system of equations into standard form (Ax + By = C) and then compare the coefficients. If the ratios of the coefficients of x and y are equal, but the constants are not, then the system has no solution.
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System 1: y = 9x + 6.25 and -18x + 2y = 12.5 In standard form: -9x + y = 6.25 and -18x + 2y = 12.5 The ratios of the coefficients of x and y are not equal, so this system could have a solution.
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System 2: y = 3x + 9 and x + 8y = 12.3 In standard form: -3x + y = 9 and x - 8y = -12.3 The ratios of the coefficients of x and y are not equal, so this system could have a solution.
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System 3: y = 4.5x - 5 and -3x + 2y = 6 In standard form: -4.5x + y = -5 and -3x + 2y = 6 The ratios of the coefficients of x and y are not equal, so this system could have a solution.
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System 4: y = -3x + 8 and 6x + 2y = -4.5 In standard form: 3x + y = 8 and 6x + 2y = -4.5 The ratios of the coefficients of x and y are equal (3/1 = 6/2), but the constants are not (8 ≠ -4.5), so this system has no solution.
Therefore, the system that has no solution is the fourth one: y = -3x + 8 and 6x + 2y = -4.5.
Similar Questions
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