Question

Solve each system by graphing.

1. -3-x=y, 4-8x=y
2. -27x-9y=3x, x=-1+y
3. 32-6x=8y, -2=2y-x
4. 2x=-16-4y, 4+5x=2y
5. 4+2y=x, x+12/7=4/7y
6. 2y+x-8=0, x+2y=-8

Answer 1

all answers and steps are shown and pictured

Answer 2

(-1, 4)

(-0.231, 0.769)

(4, 1)

(-2, -3)

(-4, -4)

No solution since graph didn't intersect at any point.

Explanation:

The pair of the linear equation of two variables is of the form:

a₁x₁ + b₁y₁ + c₁ = 0

a₂x₂ + b₂y₂ + c₂ = 0

For solving these equations we will plot the graph of these equations in the same graph paper.

Firstly we will make a value table by putting the value of one variable so, we will get the value of another variable. Now plotting these points in the graph and then join the line. Graph will be plotted.

Now, we can have three possibilities, that is:

Both lines will intersect, then we have only one solution.

both lines will coincide, then we have infinitely many solutions.

Or Both lines can be parallel i.e. they will not intersect at any point, then we have no solution to the given equation.

And the point of intersection is the solution of the graph.

The graph of given equations is plotted below.