Question

What equation is solved by the graphed systems of equations?

A. 7x+3=x+3
B. 7x-3=x-3
C. 7x+3=x-3
D. 7x-3=x+3

Answer 1

Option C: 7x + 3 = x - 3

Explanation:

We have to manually solve.

Option A:
`7x+3=x+3`

`7x - x = 3 - 3\\6x = 0\\x = 0` -------------> False

Option B:
`7x-3=x-3`

`7x-x=3-3\\6x=0\\x=0` ----------> False

Option C:
`7x+3=x-3`

`7x-x=-3-3\\6x=-6\\x=-1`--------------------> True

Option D:
`7x-3=x+3`

`7x-x=3+3\\6x=6\\x=1`--------------> False

Hence, after solving, it is shown that option C is the correct answer.

Answer 2

C. 7x +3 = x -3

Explanation:

Such an equation is graphed by resolving it into two equations:

p = q

becomes ...

y = p and y = q

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use answer choices for a clue

The left-side expression in every answer choice has an x-coefficient of 7. When those expressions are written in equation form, they match the slope-intercept form ...

y = mx +b . . . . . . . line with slope m and y-intercept b

The line with slope 7 on the graph has a y-intercept of +3. Its equation will be ...

y = 7x +3

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The right-side expression in the answer choices matches that of a line with a slope of 1. The line on the graph with a slope of 1 has a y-intercept of -3. In slope-intercept form, it is ...

y = x -3

The system of equations corresponding to the graph is ...

• y = 7x +3
• y = x -3

In the original p = q form, this is ...

7x +3 = x -3 . . . . . . . matches choice C