3. Solve. Check Your Solutions
z - 12 = 30

z = 42

Step-by-step explanation:

z - 12 = 30

Add 12 to each side

z - 12+12 = 30+12

z = 42

Check

42 - 12 = 30

30 = 30

Step-by-step explanation:

If we want to solve this algebraic equation, we need to isolate z on one side.

Add 12 to both sides:

To check our work, let's substitute 42 in as .

42 minus 12 is indeed 30.

Hope this helped!

step-by-step explanation:

(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