Question

Determine whether the given ordered pair is a solution to the system of equations.5x−y =4 x+6y =2 Ordered pair: (4,0)

Answer 1

Solution:

Given the system of equations:

$\begin{gathered} 5x-y=-4\text{ -- equation 1} \\ x+6y=2\text{ --- equation 2} \end{gathered}$

To determine if the ordered pair (4, 0) is a solution to the system of equations, we solve for x and y.

Thus, by the substitution method of solving simultaneous equations, we have

from equation 1,

$\begin{gathered} make\text{ y the subject of formula,} \\ y=5x+4---\text{ equation 3} \end{gathered}$

Substitute equation 3 into equation 2.

Thus, we have

$\begin{gathered} x+6(5x+4)=2 \\ open\text{ parentheses,} \\ x+30x+24=2 \\ collect\text{ like terms,} \\ 31x=-22 \\ divide\text{ both sides by the coefficnet of x, which is 31} \\ \frac{31x}{31}=-\frac{22}{31} \\ \Rightarrow x=-\frac{22}{31} \end{gathered}$

To solve for y, substitute the obtained value of x into equation 3.

Thus,

$y=5(-\frac{22}{31})+4=\frac{14}{31}$

Thus, the solution to the system of equations is

$(x,y)\Rightarrow(-\frac{22}{31},\frac{14}{31})$

Hence, the ordered pair (4, 0) is NOT a solution to the system of equations.