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3 years ago

What is the solution of the system? Use substitution. y = 6x + 2 3y - 18x = 12

2 answers:

5 0

3(6x+2)-18x=12 (y=6x+2, so you plug in 6x+2 into the y in 3y-18x=12)
18x+6-18x=12 (Then you distribute the 3 to the 6x and to the 2)
6=12 (Combine like terms 18x-18x)

There is no solution. Hope this helps and makes sense.

laila [671]3 years ago

3 0

Answer:

The lines are parallel so no solution exist.

Step-by-step explanation:

Given : System of equations

$y=6x+2$ and $3y-18x=12$

To find : What is the solution of the system?

Solution :

Let $y=6x+2$ ....(1)

$3y-18x=12$ ....(2)

Applying substitution method in the system of equations,

Substitute y from equation (1) into (2)

$3y-18x=12$

$3(6x+2)-18x=12$

$18x+6-18x=12$

$6\neq12$

Since by substitution we can't get the solution means either equations have no solution or both equations are parallel.

Re-write the equation (2)

$3y-18x=12$

$3(y-6x)=12$

$y-6x=4$

$y=6x+4$

Since the slope of both the equations are same.

The lines are parallel so no solution exist.

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A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, $O(0,0)$ in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

$x^2=4ay\;\cdots(i)$

where $a$ is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is $A(83, -40)$ and $B(-83, -40).$

There is only one constant in the equation of the parabola, so, use either of one point to find the value of $a$ .

Putting $A(83,-40)$ in the equation (i) we have

$83^2=4a(-40)$

$\Rightarrow a=-43.05625$

So, on putting the value of $a$ in the equation (i), the equation of bridge is

$x^2=-172.225y$

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, $x=\pm 10$ feet, put this value in equation (i) to get the value of y.