Question

Please help me...

Part A: Create at a system of liner equations with no solutions. In two or more complete sentences explain the specific characteristics that you have include in each equation to ensure that the system would not have a solution.
Part B: Using one of the equations that you created in part A create a system of liner equations that has one solution (x y)use substitution to solve the system.

Answer 1

A system of linear equations with no solution means that the lines never meet. So as long as your two lines have the same slope and different intercepts, they will be parallel.

Ex.) y= 2x + 5

and y=2x + 10

to have a solution, the lines have to cross at a point. so literally any two lines that aren't parallel.

Ex.) y= 3x + 1

to find the solution you start by setting the equations equal to each other

2x + 5 = 3x + 1

1) subtract 2x from both sides

5= x + 1

2) subtract 1 from both sides

4 = x

now we know the x value of the point is 4. To find the y value plug 4 into one of the equations

2(4) + 5

8 + 5

13

so the solution to this particular system is (4,13)