What is the solution to this system of equations?

Mathematics

1 answer:

77julia77 [94]4 years ago

6 0

Answer:

(x,y) = (3, 1/2)

Step-by-step explanation:

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations..

To solve this, add the equations;

x + 2x + 2y - 2y = 4 + 5

3x = 9

x = 3

substitute the value of x into the first equation,

3 + 2y = 4

2y = 4 -3

2y = 1

y = 1/2

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Find the area of a rectangle having a perimeter of 182 yards and a width 20 yards shorter than twice its length

Studentka2010 [4]

Let the length be $l$ in this equation.

We know that the perimeter of a rectangle is $w2 + l2 = P$

Width is defined in terms of length, so we know $w = l2 - 20$

We can substitute this value of w into the formula for perimeter to find the length.

$(l2 - 20)2 + l2 = 182$

$l4 - 40 + l2 = 182$

$l4 + l2 = 222$

$l6 = 222$

$l = 37$

So the length is 37. Now that we've found the length, we can go back to the Perimeter formula again and find width.

$w2 + (37)2 = 182$

$w2 + 74 = 182$

$w2 = 108$

$w = 54$

Width is 54. Now with both of these values found, we can calculate area with the formula $l * w = A$

$37 * 54 = A$

$1998 = A$

So the area of the rectangle is 1998 yards^2.

3 0

3 years ago

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

frosja888 [35]

Complete Question:

The given line segment has a midpoint at (3, 1). On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, -2).

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

Answer:

$y = \frac{1}{3}x$