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2 years ago

In exercises 8-10, write a system of linear equations that has the ordered pair as its solution. (-6, -2)

Mathematics

1 answer:

Anika [276]2 years ago

5 0

Answer:

(8) $x + y = -8$ and $2x - y = -10$

(9) $3x - y = -54$ and $4x + y = -30$

(10) $x + y = 2$ and $x - y = 2$

Step-by-step explanation:

Given [Missing from the question]

$(8).\ (-6,-2)\ \\ (9).\ (-12,18)\ \\ (10).\ (2,0)$

Required

Write a system of linear equations

The solutions to this question is open and have different solutions

Solving (8) (-6,-2)

Let the equations be: x + y and 2x - y

$x + y = -6 - 2$

$x + y = -8$ --- (1)

$2x - y = 2 * (-6) - (-2)$

$2x - y = -10$ -- (2)

So, the equations are:

$x + y = -8$ and $2x - y = -10$

Solving (9) (-12, 18)

Let the equations be: 3x - y and 4x + y

$3x - y = 3 *(-12) - 18$

$3x - y = -54$

$4x + y = 4 * (-12) + 18$

$4x + y = -30$

So, the equations are:

$3x - y = -54$ and $4x + y = -30$

Solving (9): (2,0)

Let the equations be: x + y and x - y

$x + y = 2 + 0$

$x + y = 2$

$x - y = 2 - 0$

$x - y = 2$

So, the equations are:

$x + y = 2$ and $x - y = 2$

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The coordinates of midpoint M and endpoint Q of a segment are M(–7, 8) and Q(–19, 30). Find the coordinates of the other endpoin

Margaret [11]

Answer:

Step-by-step explanation:

Use the midpoint formula to solve:

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

We know the midpoint and one set of coordinates, so filling those in:

$(-7,8)=(\frac{x+(-19)}{2},\frac{y+30}{2})$

Since the -7 is the x coordinate of the midpoint, we set the x part of the equation equal to -7 and solve for x, and then do the same for y. The 2 equations are:

$-7=\frac{x-19}{2}$ and $8=\frac{y+30}{2}$ We solve each one of these to get the x and y coordinates of the other endpoint. In both cases, multiply both sides of the equations by 2 and then solve by either adding or subtracting.