Question

use the substitution method to solve the system of equations choose the correct ordered pair. 2x-y=8 y=x-3 a.5,2 b.4,1 c.3,0 d.6,3

Answer 1

`\left\{\begin{array}{ccc}2x-y=8&(**)\\y=x-3&(*)\end{array}\right\\\\\text{Substitute }\ (*)\ \text{to}\ (**):\\\\2x-(x-3)=8\\2x-x-(-3)=8\\x+3=8\qquad\text{subtract 3 from both sides}\\\boxed{x=5}\\\\\text{Put the value of x to}\ (*):\\\\y=5-3\\\boxed{y=2}\\\\Answer:\ \boxed{a.\ (5,\ 2)}`

Answer 2

Solution for the given system of equations is (5,2)

Explanation:

We have been given the system of equations

`2x-y=8....(1)\\y=x-3...(2)`

On substituting the value of y from equation (2) in equation (1)

`2x-(x-3)=8`

Now, we solve the equation for x

`2x-x+3=8\\x+3=8\\x=5`

Substituting the value of x in equation (2)

`y=5-3\\y=2`

Therefore, the solution for the given system of equations is (5,2)

a is the correct option.