Caprice adds equations A and B to solve this system of equations. What makes this approach a valid method in general for solving a system of equations?
Equation A:
Equation B:
8x + 3y = 27
4x - 3y = 9
12x = 36
CLEAR
CHECK
The method will give the correct solution, x = 3 and y = 1
8(3) + 3(1) - 27
4(3)-3(1) = 9
As long as addition used on both sides or subtraction is
used on both sides, a true equation will remain true.
Because the y-terms cancel:
(8x + 3y) + (4x - 3y) - 8x + 4x + 3y - 3y = 12x
Adding a quantity like 8x + 3y to one side of an equation
and another quantity like 27 to the other side maintains
the equality if the two quantities are equal.

The function ƒ is defined by ƒ(x) = (x + 3)(x + 1). the graph of ƒ in the xy-plane is a parabola. which interval contains the x-coordinate of the vertex of the graph of ƒ?

The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.

Janie has $3. she earns $1.20 for each chore she does and can do fractions of chores. she wants to earn enough money to buy a cd for $13.50.