Solution:
Given:
A pair of linear equations
[tex]\begin{gathered} 3x+2y=-6 \\ 4x-7y=-8 \end{gathered}[/tex]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,
[tex]\begin{gathered} 3x+2y=-6\ldots\ldots\ldots\ldots\ldots(1)\times7 \\ 4x-7y=-8\ldots\ldots\ldots\ldots\ldots\text{.}(2)\times2 \\ \\ \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=-\frac{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=\frac{0}{-4} \\ y=0 \\ \\ \text{Hence, the solution is } \\ x=-2 \\ y=0 \\ \\ \text{Thus,} \\ (x,y)=(-2,0) \end{gathered}[/tex]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).
