MATH SOLVE

4 months ago

Q:
# Which of these statements is correct?The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Accepted Solution

A:

Answer:The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.Step-by-step explanation:1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.Solve these linear equations simultaneouslyStep 1 : Find y in terms of x from any one equation6x - 5y = 8y = 8 - 6x -5Step 2 : Substitute y in terms of x from step 1 in the second equation.16x - 6y = 2216x - 6 (8 - 6x) = 22 -580x - 48 + 36x = 22 x -594x = 43x = 0.457This statement is incorrect as it does have a solution.2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.Solve these linear equations simultaneouslyStep 1 : Find y in terms of x from any one equation7x + 2y = 6y = 6 - 7x 2Step 2 : Substitute y in terms of x from step 1 in the second equation.14x + 4y = 1614x + 4(6 - 7x) = 16 214x + 12 - 14x = 160 ≠ 4This statement is not true as there are no solutions.3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.Solve these linear equations simultaneouslyStep 1 : Find x in terms of y from any one equation8x - 3y = 10x = 10 + 3y 8Step 2 : Substitute x in terms of y from step 1 in the second equation.16x - 6y = 2216(10 + 3y) - 6y = 22 820 + 6y - 6y = 20 ≠ -18This statement is true because there are no solutions4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.Solve these linear equations simultaneouslyStep 1 : Find x in terms of y from any one equation9x + 6y = 14x = 14 - 6y 9Step 2 : Substitute x in terms of y from step 1 in the second equation.18x + 12y = 2618 (14 - 6y) + 12y = 26 98 - 12y + 12y = 260 ≠ 18This statement is incorrect because there are no solutions. It does not have infinite number of solutions.!!