Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Start with the given system of equations:

system(x-2y=-8,3x+4y=6)

In order to graph these equations, we must solve for y first.

Let's graph the first equation:

x-2y=-8

Start with the first equation.

-2y=-8-x

Subtract

from both sides.

y=(-8-x)/(-2)

Divide both sides by

to isolate

Rearrange the terms and simplify.

Now let's graph the equation:

drawing(500,500,-10,10,-10,10, 
grid(0), 
graph(500,500,-10,10,-10,10,(1/2)x+4) 
)

Graph of

.

-------------------------------------------------------------------

Now let's graph the second equation:

3x+4y=6

Start with the second equation.

4y=6-3x

Subtract

from both sides.

y=(6-3x)/(4)

Divide both sides by

to isolate

Rearrange the terms and simplify.

Now let's graph the equation:

drawing(500,500,-10,10,-10,10, 
grid(0), 
graph(500,500,-10,10,-10,10,-(3/4)x+3/2) 
)

Graph of

.

-------------------------------------------------------------------

Now let's graph the two equations together:

drawing(500,500,-10,10,-10,10, 
grid(1), 
graph(500,500,-10,10,-10,10,(1/2)x+4,-(3/4)x+3/2) 
)

Graph of

(red). Graph of y=-(3/4)x+3/2

(green)

From the graph, we can see that the two lines intersect at the point

. So the solution to the system of equations is

. This tells us that the system of equations is consistent and independent.