Question

Determine if the given ordered pair is the solution of the system of equations.1. (1, 2) x+y=32x-3y= -4 ___

Answer 1

The Solution:

We are required to determine if the given ordered pair attached to each pair of equations is the solution of the system of equations.

1.

$\begin{gathered} x+y=3 \\ 2x-3y=-4\text{ } \\ \text{(1,2)} \end{gathered}$

We shall substitute 1 for x and 2 for y.

$\begin{gathered} 1+2=3 \\ 2(1)-3(2)=2-6=-4 \\ \text{ So, (1,2) is the solution.} \end{gathered}$

2.

$\begin{gathered} 2x-y=-10 \\ x-3y=2\text{ } \\ \text{(-4,2)} \end{gathered}$

Substitute -4 for x and 2 for y.

$\begin{gathered} 2(-4)-2=-8-2=-10 \\ -4-3(2)=-4-6=-10\ne2 \\ \text{ Hence, (-4,2) is not a solution.} \end{gathered}$

3.

$\begin{gathered} x-y=-1 \\ 2x=y+4 \\ (5,6) \end{gathered}$

Here, x=5, y=6

$\begin{gathered} 5-6=-1 \\ 2(5)=6+4 \\ 10=10 \\ \text{ So, (5,6) is a solution.} \end{gathered}$

Therefore, system1 is a solution

system 3 is not a solution.

system5 is a solution.