Question

Determine whether the ordered pair is a solution to the given system of linear equations.(1,2) 3x-y=12x+3y=8

Forms of linear equations

Determine whether the ordered pair is a solution to the given system of linear equations.
(1,2)
$$\left\{\begin{matrix} 3x−y=1 \\ 2x+3y=8 \end{matrix}\right\}$$

2020-10-24

Consider the system of equations as:
1) $$3X−Y=1$$
2) $$2X+3Y=8$$
Verify if ordered pair (1,2) is solution of (1) and (2).
Substitute $$X=1$$ and $$Y=2$$ in equation (1).
$$3(1)−2\underset{=}{?}1$$
$$3−2\underset{=}{?}1$$
$$1=1$$ (True)
Hence, (1,2) satisfies the equation (1).
Substitute $$X=1$$ and $$Y=2$$ in equation (2).
$$2(1)+3(2)\underset{=}{?}8$$
$$2+6\underset{=}{?}18$$
$$8=8$$ (True)
Hence, (1,2) satisfies the equation (2).
Hence, the ordered pair (1,2) is a solution to the given system of linear equations.