Plz ! i've been having trouble with these

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:

   

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .