How do you find the x and y intercept of 3x − y = 5 3xy=5?

1 Answer
Jul 7, 2016

x_("intercept")=5/3xintercept=53

y_("intercept")=-5yintercept=5

Explanation:

color(blue)("Determine "y_("intercept"))Determine yintercept

The y-axis crosses the x-axis at x=0x=0 so to find the y-intercept substitute x=0x=0 into the equation

color(brown)(3x-y=5)color(blue)(" "->" "3(0)-y=53xy=5 3(0)y=5

But 3xx0=03×0=0 giving

-y=5y=5

Multiply both sides by (-1)(1)

(-y)xx(-1)=5xx(-1)(y)×(1)=5×(1)

y=-5y=5
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color(blue)("Determine "x_("intercept"))Determine xintercept

The x-axis crosses the y-axis at y=0y=0 so to find the x-intercept substitute y=0y=0 into the equation

color(brown)(3x-y=5)color(blue)(" "->" "3x-0=53xy=5 3x0=5

color(brown)(3x=5)3x=5

Divide both sides by color(blue)(3)3

color(brown)(3/(color(blue)(3)) xx x=5/(color(blue)(3))33×x=53

But 3/3=133=1

x=5/3x=53

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color(brown)(3x-y=5)" "->" "color(blue)(y=3x-5)3xy=5 y=3x5
Tony B