Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the solutions of the equation 4-x = 2x + 3.

Part B: Make tables to find the solution to 4-x = 2x + 3. Take the integer values of x between -3 and 3.
Part C: How can you solve the equation 4-x = 2x + 3 graphically?

Answer 1

Hope it cleared your doubt.

Answer 2

Explanation:

We have been given two equations:

`y=4-x`

And
`y=2x+3`

Part A: The solution to the equation is the point where they intersect because both lines will satisfy the given equation at that intersection point.

Part B: Now, we will solve
`4-x=2x+3`

Collect like terms on one side of the equation so we get:

`2x+x=4-3`

`\Rightarrow 3x=1`

`\Rightarrow x=(1)/(3)`

Part C: we have to solve the equation graphically please look at the attachment for the solution graphically.

The intersection point is the solution of the two equations.