Question

A pair of equations is shown below.

x + y = 5
y = one halfx + 2

If the two equations are graphed, at what point do the lines representing the two equations intersect?

(2, 5)
(5, 2)
(2, 3)
(3, 2)

Answer 1

Graph the two problems here:
https://www.desmos.com/calculator
And figure out where they intersect, you can also solve by using substitution

Answer 2

according to the observation of @pooja195 if I substitute the value of \(y\) from second equation, into the first one, I get:
\[\huge x + \left( {\frac{x}{2} + 2} \right) = 5\]
please solve for \(x\)

Answer 3

x=2

Answer 4

that's right!

Answer 5

now, please replace \(x=2\) into the second equation, you should get this:
\[\huge y = \frac{x}{2} + 2 = \frac{2}{2} + 2 = ...?\]

Answer 6

b

Answer 7

in option B, we have \(x=5\), and not \(x=2\)

Answer 8

so whats the correct answer

Answer 9

no, please here is another hint:
\[\huge y = \frac{x}{2} + 2 = \frac{2}{2} + 2 = 1 + 2 = ...?\]

Answer 10

so, \(y=...?\)

Answer 11

A

Answer 12

I got \(y=3\), so, what is the right option?

Answer 13

if \(x=2\) and \(y=3\) then the solution is given by the ordered pair \((2,3)\)

Answer 14

c

Answer 15

that's right!