Asystem of equations is shown below. which of the following statements describes the graph of this system of equations in the (x, y) coordinate plane?
3y − 5x = 15
6y − 10x = 30
a. two parallel lines with positive slope
b. two parallel lines with negative slope
c. a single line with positive slope
d. a single line with negative slope
The given system of equations represent a single line with positive slope. Option C is correct
Given, a system of equations which are shown below,
3y − 5x = 15 ⇒ (1)
6y − 10x = 30 ⇒ (2)
When we observe the above equations, when first equation is multiplied with 2, it results in second equation
Eqn 1 multiplied with "2" , we get
⇒ 6x - 10x = 30 ⇒ eqn 3
If we notice eqn 2 and eqn 3 are same.
Which means the two line equations represents the same line.
Now let us find the slope of line.
So, the line has a positive slope. Thus the given system of equations represent a single line with positive slope. So option C is correct.
3y - 5x = 15 ... A
y = 5/3 * X +15 slope 3/5 , y intercept 15
6y - 10x =30
(6y - 10x) /2 = 30 / 2
3y - 5x = 15 ... B
y = 5/3 * x + 15 slope 3/5 , y intercept 15
∴ Answer is C
Option A. Two parallel lines with positive slope.
An equation of a straight line is written as:
ay = mx + c
where a = is the coefficient of y
m = the gradient of the line
c = y -intercept
Examining the two equations:
3y − 5x = 15 ...1
6y − 10x = 30 ...2
The equations can be rearranged as follows:
3y = 5x + 15
6y = 10 x + 30 or 2 (3y = 5 x + 15)
As seen from the expression, the equation (2) is twice the equation (1)
In addition, the equations are equal if (2) is reduced to lowest terms.
The gradients will be equal.
The equations are parellel (equal gradient) with a positive slope (5 and 10 respectively)
Option C. will be correct.
The equations of straight lines are given as
3y - 5x = 15 ........... (1)
And, 6y - 10x = 30 ......... (2)
If we divide the equation (2), by 2 then we will get 3y - 5x = 15 which is nothing but the equation (1).
Therefore, those two equations (1) and (2) represents the same straight line.
Now, from equation (1), we can write .
This is an equation of a straight line in slope-intercept form and here slope is positive.
Therefore, Option C. will be correct. (Answer)
parallel lines have the same slope
The given system of equations represent a single line with positive slope. So option C is correct.
Given system of equations are
Now, if we observe, multiplying the equation with 2 results in equation.
which means the two line equations represents the same line.
Now, let us find the slope of line,
So, the line has a positive slope.
step-by-step explanation: g=6
283 square feet