You can see that the term $-6y$ appears in both equations. In this cases, we can leverage this peculiarity and subtract the two equations to get rid of the repeated term. So, if we subtract the first equation from the second, we have

$(-4x -6y) - (-10x-6y) = 54-0 \iff 6x = 54 \iff x = 9$

Now that we know the value of $x$ , we can substitute in any of the equation to deduce the value of $y$ : if we use the first equation, for example, we have

$-10x-6y=0 \iff -10\cdot 9 - 6y = 0 \iff -90-6y=0 \iff 6y = -90 \iff y = -15$

7 0

3 years ago

About 786,700,000 passengers traveled by plane in the United States in 2010. What is

Schach [20]

Answer: 7.867 x 10^8

Step-by-step explanation:

(the “^8” is an exponent of 8)

4 0

3 years ago

Find another name for the given number but with the denominator indicated use multiplying by 1. 1/2 = ?/10

liq [111]

5/10 because it is equivalent to 1/2

So the answer is 5/10

6 0

3 years ago

Give the equation of the line perpendicular to y +7= -2(x - 6) through the<br> point (6,-3)

lilavasa [31]

<u>Note: this answer assumes the equation of the line can be put in slope-intercept form. </u>

Answer:

$y + 3 = \frac{1}{2}(x-6)$

Step-by-step explanation:

1) First, find the slope of y + 7 = -2 (x - 6). We can see that it's already in point-slope form, or $y-y_1 = m (x-x_1)$ format. Remember that the number in place of the $m$ is the slope. Therefore, -2 is the slope of that equation.

What we need is the slope that is perpendicular to that, though. So, find the opposite reciprocal of -2. To do this, change its sign, convert it into a fraction ( $-\frac{2}{1}$ ), and flip its numerators and denominators. Therefore, the perpendicular slope would be $\frac{1}{2}$ .

2) Now that we have a slope and a point the line passes through, we can write an equation using the point-slope formula, $y-y_1 = m (x-x_1)$ . In order to write an equation, the $x_1$ , $y_1$ , and $m$ have to be substitute for with real values.

The $m$ represents the slope. We already calculated that in the last step, so put $\frac{1}{2}$ in place of the $m$ . The $x_1$ and $y_1$ represent the x and y values of a point the line passes through. We know that the line has to pass through (6, -3), so substitute 6 for $x_1$ and -3 for $y_1$ :

$y - (-3) = \frac{1}{2}(x -(6))\\y + 3 = \frac{1}{2}(x - 6)$

Therefore, (again, assuming that the line can be put in point-slope form) the answer is $y + 3 = \frac{1}{2}(x-6)$ .

5 0

3 years ago