Solve the formula for the variable y: 5x+2y=10

The process is to go step-by-step to isolate the y.

To do this, you basically run the order of operations in reverse.

In 5x+2y=10, the first thing to move away from the left side is 5x and  you cancel it out by subtracting 5x from both sides:

    5x+2y - 5x = 10 - 5x

The 5x's on the left cancel leaving you with:  

   2y = 10 - 5x

Side note: this is more commonly written as 2y = -5x+10, since we tend to write variable terms first.

Finally, to get the y fully by itself, you need to cancel the 2 that's multplied against it.  To cancel multiplication, you need to divide:

The most important thing to remember here is that the 2 needs to divide into both terms on the right:

Finally, we simplify this into:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3