Answer:
The coordinates that satisfy the equations will be: (3, 2)
Hence, option C is correct.
Step-by-step explanation:
Given the equations
[tex]x\:-2y\:=-1;\:2x\:+\:3y=12[/tex]
solving the equations to find the solution values (coordinates)
[tex]\begin{bmatrix}x-2y=-1\\ 2x+3y=12\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}x-2y=-1\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2x-4y=-2[/tex]
[tex]\begin{bmatrix}2x-4y=-2\\ 2x+3y=12\end{bmatrix}[/tex]
[tex]2x+3y=12[/tex]
[tex]-[/tex]
[tex]\underline{2x-4y=-2}[/tex]
[tex]7y=14[/tex]
so
[tex]\begin{bmatrix}2x-4y=-2\\ 7y=14\end{bmatrix}[/tex]
solve for y
[tex]7y=14[/tex]
[tex]y=2[/tex]
[tex]\mathrm{For\:}2x-4y=-2\mathrm{\:plug\:in\:}y=2[/tex]
[tex]2x-4\cdot \:2=-2[/tex]
[tex]2x=6[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]\frac{2x}{2}=\frac{6}{2}[/tex]
[tex]x=3[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=3,\:y=2[/tex]
Therefore, the coordinates that satisfy the equations will be: (3, 2)
Hence, option C is correct.
