Question

Consider this system of equations.  x + 2y = 5,  –x + 3y = 6 The x- and y-intercepts of the first equation are found below. x-intercept: y-intercept: x + 2(0) = 5 x = 5 (5, 0) (0) + 2y = 5 2y = 5 y = 52 = 2.5 Find the intercepts for the equation –x + 3y = 6. What is the x-intercept? What is the y-intercept?

Answer 1

x-intercept

is (-6,0)

y-intercept

is (0,2)

Explanation:

Answer 2

Part 1) The x-intercept is the point (-6,0)

Part 2) The y-intercept is the point (0,2)

Explanation:

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

we have

`-x+3y=6`

Part 1) Find the x-intercept

For y=0

substitute the value of y in the linear equation and solve for x

`-x+3(0)=6`

`-x=6`

`x=-6`

The x-intercept is the point (-6,0)

Part 2) Find the y-intercept

For x=0

substitute the value of x in the linear equation and solve for y

`-(0)+3y=6`

`3y=6`

`y=2`

The y-intercept is the point (0,2)