For the solutions to the equation
the solutions are
x = -6 and x = -4
solving an equation graphically means to graph out both sides of the equation and use the x-coordinates of intersection points as the solutions to the equations. this is because those are x-values result in making the original equation have both sides by equal to each other. the y-coordinate of each graph is the result of putting in that certain x-value.
the metal worker should combine
50 g of the 5% tin alloy
50 g of the 45% tin alloy
how to solve this:
x and y are respectively the grams of the 5% and 45% tin alloys.
we are told that the metal worker needs 100 grams in total. this means that
x + y = 100
since x and y are the grams.
the worker also needs that 100g to be 25% tin.
x represents grams of the 5% tin alloy.
5% in decimal format is 0.05.
if we multiply x by 0.05, we get the grams of the tin that are in the 5% tin alloy. 5% of those grams are tin grams.
so 0.05x is the grams of tin from the 5% tin alloy.
y represents the grams of the 45% tin alloy.
45% in decimal format is 0.45.
if we multiply y by 0.45, we get the grams of the tin that are in the 45% tin alloy. 45% of those grams are tin grams.
so 0.45y is the grams of tin from the 45% tin alloy.
we are told that the final amount of tin is 25% of the 100 g of bronze.
so the final amount of tin should be 100*0.25, which is 25.
therefore
0.05x + 0.45y = 25
this is the system in question; the x- and y-values must satisfy both equations:
we can solve this by linear combinations.
multiply both sides of the top equation by -0.05 so that we get 0.05x and -0.05x
add both equations:
combine the like terms together
use either of the equations to solve for x with this y-value.
use the simpler one, equation (i):
so 50 grams of both alloys.
can check answer to see if they satisfy the system:
