Question

For each ordered pair, determine whether it is a solution to the system of equations. 3x + 2y = -6 4x - 7y= -8 Is it a solution? (x, y) X X Yes No (-8, 9) (5, 4) (6, -3) (-2,0)

Answer 1

Given:

A pair of linear equations

`\begin{gathered} 3x+2y=-6 \\ 4x-7y=-8 \end{gathered}`

The solution to the system of equations is gotten by solving for the unknowns (x and y) simultaneously.

Solving for the solution using the elimination method,

`\begin{gathered} 3x+2y=-6\ldots\ldots\ldots\ldots\ldots(1)*7 \\ 4x-7y=-8\ldots\ldots\ldots\ldots\ldots\text{.}(2)*2 \\ \\ \text{This now becomes;} \\ 21x+14y=-42 \\ 8x-14y=-16 \\ \\ \text{Adding the two equations up;} \\ 21x+8x+14y+(-14y)=-42+(-16) \\ 29x+14y-14y=-42-16 \\ 29x=-58 \\ \text{Dividing both sides by 29 to get x,} \\ x=-(58)/(29) \\ x=-2 \\ \\ \text{Substituting the value of x in any of the equations to get y,} \\ 8x-4y=-16 \\ 8(-2)-4y=-16 \\ -16-4y=-16 \\ -4y=-16+16 \\ -4y=0 \\ \text{Dividing both sides by -4 to get the value of y,} \\ y=(0)/(-4) \\ y=0 \\ \\ \text{Hence, the solution is } \\ x=-2 \\ y=0 \\ \\ \text{Thus,} \\ (x,y)=(-2,0) \end{gathered}`

Alternatively, solving the systems of equations using graphical method, the solution is seen at the point of intersection of the two lines as shown below;

Therefore, the solution to the system of equations as an ordered pair (x,y) is (-2,0).