Question

Fiona wrote the linear equation y = x-5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona's. Which equation could be Henry's? 1) x - 2y = 25 2) x - 2y = 25 3) x - ²y = 25 4) x - ²y = 25

Answer 1

The equation that could be Henry's is x - ²y = 25 (option 4). It has the same solution as Fiona's equation, y = x-5.

Step-by-step explanation:

The equation that could be Henry's is x - ²y = 25 (option 4).

This equation has the same solution as Fiona's equation, y = x-5, because the coefficients of x and y are the same.

By rewriting Henry's equation in slope-intercept form, we get y = -1/2x + 25/2. This equation has a slope of -1/2 and a y-intercept of 25/2.

Answer 2

Henry's equation with the same solutions as Fiona's
`\(y = (2)/(5)x - 5\)` is Option B:
`\(x - (5)/(2)y = (25)/(4)\)`.

Let's start by rewriting Fiona's equation in a more standard form, which is the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:

Fiona's equation:
`\(y = (2)/(5)x - 5\)`

Comparing Fiona's equation with the standard form, we can see that the slope of her equation is
`\(m = (2)/(5)\)`.

For Henry's equation to have all the same solutions as Fiona's, it needs to have the same slope and different constants. Let's check the given options:

Given Options:

A.
`\(x - (5)/(4)y = (25)/(4)\)`

B.
`\(x - (5)/(2)y = (25)/(4)\)`

C.
`\(x - (5)/(4)y = (25)/(2)\)`

D.
`\(x - (5)/(2)y = (25)/(2)\)`

Analyzing Henry's Equation:

The slope-intercept form of Henry's equation should have the same slope as Fiona's
`(\((2)/(5)\))`. Let's rearrange the given options to see their slope-intercept forms:

A.
`\(x - (5)/(4)y = (25)/(4)\)` rearranges to
`\(y = (4)/(5)x - (5)/(4)\)`. This equation doesn't match Fiona's equation.

B.
`\(x - (5)/(2)y = (25)/(4)\)` rearranges to
`\(y = (2)/(5)x - (5)/(2)\)`. This equation matches Fiona's equation.

C.
`\(x - (5)/(4)y = (25)/(2)\)` rearranges to
`\(y = (4)/(5)x - (25)/(4)\)`. This equation doesn't match Fiona's equation.

D.
`\(x - (5)/(2)y = (25)/(2)\)` rearranges to
`\(y = (2)/(5)x - (25)/(2)\)`. This equation doesn't match Fiona's equation.

Therefore, among the given options, Option B
`(\(x - (5)/(2)y = (25)/(4)\))` represents an equation that has the same solutions as Fiona's equation
`\(y = (2)/(5)x - 5\)`.

Question:

Fiona wrote the linear equation
`\(y = (2)/(5)x - 5\)`. When Henry wrote his equation they discovered that his equation had all the same Solutions as fionas. which equation could have been Henry's.

A.
`\(x- (5)/(4)x = (25)/(4) \)`

B.
`\(x- (5)/(2)x = (25)/(4) \)`

C.
`\(x- (5)/(4)x = (25)/(2) \)`

D.
`\(x- (5)/(2)x = (25)/(2) \)`