Question

A pair of equations is shown below: y = 4x – 5 y = 3x + 4 What is the solution to the pair of equations? (9, 31) (–9, 31) (–9, –31) (9, –31)

Answer 1

Y=4x-5
Y=3x+4
Plug in each choice:
(9,31)
31=4(9)-5 ——— 31=36-5 TRUE

31=3(9)+4——— 31=27+4 TRUE

(9,31) must be the answer but let's try the other choices to be sure...
(-9,31)
31=4(-9)-5 ——— 31=-36-5... =-41 FALSE

(-9,-31)
-31=4(-9)-5 ——— -31= -36-5...=-41 FALSE

(9,-31)
-31= 4(9)-5 ——— -31= 36-5... =31 FALSE

SO THE CORRECT ANSWER = (9,31)

Answer 2

Equation 1)  y = 4x - 5
Equation 2)  y = 3x + 4

For equation 1, subtract 4x from both sides so that x and y are on the same side

1)  -4x + y = -5

For equation 2, subtract 3x from both sides so that x and y are on the same side.

2)  -3x + y = 4
1)  -4x + y = -5

Subtract the equations from one another.

-x = -9

x = 9

Plug in 9 for x in the first equation.

-4x + y = -5

-4(9) + y = -5

Simplify.

-36 + y = -5

Add 36 from both sides.

y = -5 + 36

Simplify.

y = 31

So, your solution is :

(9, 31)

~Hope I helped!~