solve the linear system by graphing

Question

solve the linear system by graphing and check the solution.

 

y = x + 1

y = -3x + 9

 

how will this look on a graph?

Answer 1

Graphing linear systems is pretty mindless once you have the process.

1) Find the y intercept where x=0.

y = x + 1 --> (0,1)

y = -3x + 9 --> (0,9)

2) Find the x intercept where y =0

y = x +1 --> (-1,0)

y = -3x + 9 --> (3,0)

3) Draw the appropriate scaling for x and y. We know that y has to go up to 9 and x has to go down to -1.

4) Connect the dots.

Draw a line between (0,1) and (-1,0).

Draw a line between (0,9) and (3,0).

 

 

Answer 2

Hi again L;

y = x + 1
y = -3x + 9

Both equations are in SLOPE-INTERCEPT FORMAT...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

FIRST EQUATION...

y = x + 1
Slope, m, is 1.

Y-intercept, b, is 1.

SECOND EQUATION...

y = -3x + 9

Slope, m, is -3.

Y-intercept, b, is 9.

It would be helpful to know at what point the two lines intersect.  Let's subtract the second equation from the first.  We could subtract the first equation from the second.  I randomly select this arrangement...

y = x + 1
-(y = -3x + 9)

0=4x-8

Let's subtract 4x from both sides...

-4x+0=4x-4x-8

-4x=-8

x=2

Let's plug-in x into either equation to solve for y.  I randomly select the first...

y = x + 1
y=2+1

y=3

Let's check our results with the second equation...

y = -3x + 9

3=[(-3)(2)]+9

3=-6+9

3=3

The lines intersect at coordinate (2,3).