Question

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

Answer 1

Answer:

The correct option is 2.

Step-by-step 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.

$0=-4x+19\Rightarrow x=\frac{19}{4}=4.75$

$0=2x+1\Rightarrow x=\frac{-1}{2}=-0.5$

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.

Answer 2

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:

$4x - - 2x = 4x + 2x = 6x$

$19 - 1 = 18$

$6x = 18$

$x = 18 \div 6 = 3$

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.