Question

What is the solution to the equation 3x-5y=7?

Answer 1

(n, 0.6n-1.4)

Step-by-step explanation:

3x-5y=7 is a linear equation, we can find y in terms of x.

5y=3x-7

y=0.6x-1.4

so, the solutions are (n, 0.6n-1.4) for any real number n.

Answer 2

The solution to the equation
`\(3x - 5y = 7\)`can be expressed in terms of
`\(y\)` as \
`(y = (3)/(5)x - (7)/(5)\).`

Step-by-step explanation:

To find the solution to the equation
`\(3x - 5y = 7\),` we can rearrange it to isolate
`\(y\).` Subtracting
`\(3x\)` from both sides gives
`\(-5y = -3x + 7\),` and dividing both sides by
`\(-5\)` yields
`\(y = (3)/(5)x - (7)/(5)\).` This form,
`\(y = mx + b\),` is the equation of a line in slope-intercept form, where
`\(m\)` is the slope and
`\(b\)` is the y-intercept.

The slope of the line is the coefficient of
`\(x\)` , which is
`\((3)/(5)\)` , indicating that for every unit increase in
`\(x\), \(y\)`increases by
`\((3)/(5)\)` units. The y-intercept is
`\(-(7)/(5)\)` , representing the point where the line crosses the y-axis.

Understanding how to manipulate the equation of a line to slope-intercept form provides insights into the characteristics of the line, including its slope and y-intercept. This information is valuable for interpreting the relationship between the variables and graphing the line on a coordinate plane.