Question

A system 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

Select one:
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

Answer 1

C

Explanation:

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

Answer 2

Option A. Two parallel lines with positive slope.

Explanation:

Thinking process:

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)