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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

[tex]4x + y = 19[/tex]

[tex] - 2x + y = 1[/tex]

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

[tex]4x - - 2x = 4x + 2x = 6x[/tex]

[tex]19 - 1 = 18[/tex]

[tex]6x = 18[/tex]

[tex]x = 18 \div 6 = 3[/tex]

So the x coordinate is 3.

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

[tex]y = 2x + 1 = 2(3) + 1 = 7[/tex]

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

Answer:

The correct option is 2.

Step-by-step explanation:

The given system of equations is

[tex]y=-4x+19[/tex]           ..... (1)

[tex]y=2x+1[/tex]               ..... (2)

The slope intercept form of a line is

[tex]y=mx+b[/tex]             .... (3)

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

From (1) and (3), we get

[tex]m=-4,b=19[/tex]

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

[tex]m=2,b=1[/tex]

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.

[tex]0=-4x+19\Rightarrow x=\frac{19}{4}=4.75[/tex]

[tex]0=2x+1\Rightarrow x=\frac{-1}{2}=-0.5[/tex]

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

[tex]-4x+19=2x+1[/tex]

[tex]19-1=2x+4x[/tex]

[tex]18=6x[/tex]

Divide both sides by 6.

[tex]3=x[/tex]

Put this value in equation (1).

[tex]y=-4(3)+19=-12+19=7[/tex]

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

Hence the correct option is 2.

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