Question

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

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

Answer 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

`4x + y = 19`

`- 2x + y = 1`

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

`4x - - 2x = 4x + 2x = 6x`

`19 - 1 = 18`

`6x = 18`

`x = 18 / 6 = 3`

So the x coordinate is 3.

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

`y = 2x + 1 = 2(3) + 1 = 7`

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

Answer 2

The correct option is 2.

Explanation:

The given system of equations is

`y=-4x+19` ..... (1)

`y=2x+1` ..... (2)

The slope intercept form of a line is

`y=mx+b` .... (3)

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

From (1) and (3), we get

`m=-4,b=19`

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

`m=2,b=1`

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.

`0=-4x+19\Rightarrow x=(19)/(4)=4.75`

`0=2x+1\Rightarrow x=(-1)/(2)=-0.5`

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

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

`19-1=2x+4x`

`18=6x`

Divide both sides by 6.

`3=x`

Put this value in equation (1).

`y=-4(3)+19=-12+19=7`

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

Hence the correct option is 2.