The answer is: [A]: "No solution" . _______________________________________________ Note: Given: _______________________________________________ y = 4x + 8 ; y = 4x + 2 ; _______________________________________________
Since: "y = y" ;
4x + 8 = 4x + 2 ; which is not true; ______________________________ 4x + 8 ≠ 4x + 2 ; since, "8 ≠ 2" ;
Note: Suppose: "4x + 8 = 4x + 2" ;
→ Subtract "4x" from each side of the equation:
4x + 8 − 4x = 4x + 2 − 4x ;
to get: _________________ " 8 = 2 " ; not true ; since "8 ≠ 2" ; ______________________________ Also, suppose: _______________________________ 4x + 8 = 4x + 2 ;
→ Subtract "2" from BOTH SIDES of the equation;
4x + 8 − 2 = 4x + 2 − 2 ;
to get:
4x + 6 = 4x
(Note: "4x + 0 = 4x" ; but "4x + 6 ≠ 4x") l
But even if we have:
4x + 6 = 4x ;
→ Subtract "4x" from EACH side of the equation:
4x + 6 − 4x = 4x − 4x ;
to get:
6 = 0 ; which is not true; "6 ≠ 0" . ____________________________________ The correct answer is: [A]: "No solution" . ______________________________________
You would isolate one of the variables and then plug the expression into the other equation to find the value of one variable. Then you would plug this value into the other equation to determine the value of the remaining variable.
x for how much one cookie costs and y for how much one doughnut costs 6x+4y=3.5 12x+5y=5.23
solve by substitution: (elimination would work too) 4y=3.5-6x y=0.875-1.5x 12x+5(0.875-1.5x)=5.23 12x+4.375x-7.5x=5.23 4.5x=0.855 x=0.19 now use x to solve for y: 6(0.19)+4y=3.5 1.14+4y=3.5 2.36=4y y=0.59
