Question

An unknown number w is 30 more than an unknown number p. The number w is also p less than 5. The equations to find p and w are shown below:

w = p + 30
w = −p + 5

Which is a correct step to find p and w?

Add the equations to eliminate p.
Multiply the equations to eliminate w.
Write the points where the graphs of the equations intersect the x-axis.
Write the points where the graphs of the equations intersect the y-axis.

Answer 1

Answer: The correct option is (A) Add the equations to eliminate p.

Step-by-step explanation: Given that an unknown number w is 30 more than an unknown number p. The number w is also p less than 5. The equations to find p and w are shown below:

`w=p+30~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\w=-p+5~~~~~~~~~~~~~~~~~~~~~~~(ii)`

We are to select the correct step to find p and w.

Since the co-efficient of p is 1 and -1 in equations (i) and (ii) respectively, so adding both the equations will eliminate p, and we will get the value of w.

Then, substituting the value of w in any one of the equations will give us the value of p.

So, the system of equations is solved as follows :

Adding equations (i) and (ii), we get

`w+w=30+5\\\\\Rightarrow 2w=35\\\\\Rightarrow w=17.5.`

Substituting the value of w in equation (i), we get

`p=w-30=17.5-30=-12.5.`

Thus, the correct step is the add the equations to eliminate p.

Option (A) is CORRECT.

Answer 2

The given equations are

`w = p+30 \\ w = -p+5`

TO solve for p and w, we can use elimination method. And the first step is to eliminate p by adding both equations .

So out of the given options, correct option is the first option .