Which graph best represents the solution to the system of equations shown below?

y = -4x + 19
y = 2x + 1

First find the x and y values because where the lines will intersect, they share the point of the intersection so they will share the x and y coordinates.

Rearrange equations

To cancel y, we must do equation 1 minus equation 2. Similarly:

So the x coordinate is 3.

The y coordinate can be found with substitution of x into one of the equations:

So where the two lines intersect is at the point (3, 7), which is the solution to the equations.

The correct option is 2.

Step-by-step explanation:

The given system of equations is

          ..... (1)

              ..... (2)

The slope intercept form of a line is

            .... (3)

where, m is slope and b is y-intercept.

From (1) and (3), we get

The slope of first line is -4 and the y-intercept is 19. It means it is a decreasing line and intersect the y-axis at (0,19).

From (2) and (3), we get

The slope of first line is 2 and the y-intercept is 1. It means it is an increasing line and intersect the y-axis at (0,1).

Put y=0, to find the x-intercepts.

Therefore the x-intercept of first line is 4.75 and the x-intercept of the second line is -0.5.

Only the second graph satisfy all the above condition.

One solving the given equation we get

Divide both sides by 6.

Put this value in equation (1).

Therefore the solution of the given system of equation is (3,7).

Hence the correct option is 2.

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: