Question

Is (3,8) a solution to this system of equations?y=7x+8y=x+1-True-False

Equations

Is (3,8) a solution to this system of equations?
$$y=7x+8$$
$$y=x+1$$
-True
-False

2021-02-15

Step 1 : Analysis
Given :
$$y =7x+8$$
$$y=x+1$$
Step 2 : Simplification
We have,
$$y=7x+8...(1)$$
$$y=x+1...(2)$$
If (3,8) is a solution of the system of equations then x=3 and y=8 must satisfy the equation (1) and (2).
Step 3 : Solution
Substituting $$x=3$$ and $$y=8$$ in the equation (1),
$$\displaystyle{8}={7}\times{3}+{8}$$
$$8=21+8$$
$$8=29$$
which is an absurd result since $$\displaystyle{8}\neq{29}$$  so (3,8) does not satisfy the equation (1).
Therefore the (3,8) is not a solution to the system of equations.