Question

Select the correct answer. Which set of coordinates satisfies the equations x − 2y = -1 and 2x + 3y = 12? A. (1, 2) B. (3, 1) C. (3, 2) D. (-3, -2) E. (3, -2)

Answer 1

Answer:

3,2

Step-by-step explanation:

Answer 2

Answer:

The coordinates that satisfy the equations will be: (3, 2)

Hence, option C is correct.

Step-by-step explanation:

Given the equations

$x\:-2y\:=-1;\:2x\:+\:3y=12$

solving the equations to find the solution values (coordinates)

$\begin{bmatrix}x-2y=-1\\ 2x+3y=12\end{bmatrix}$

$\mathrm{Multiply\:}x-2y=-1\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2x-4y=-2$

$\begin{bmatrix}2x-4y=-2\\ 2x+3y=12\end{bmatrix}$

$2x+3y=12$

$-$

$\underline{2x-4y=-2}$

$7y=14$

so

$\begin{bmatrix}2x-4y=-2\\ 7y=14\end{bmatrix}$

solve for y

$7y=14$

$y=2$

$\mathrm{For\:}2x-4y=-2\mathrm{\:plug\:in\:}y=2$

$2x-4\cdot \:2=-2$

$2x=6$

$\mathrm{Divide\:both\:sides\:by\:}2$

$\frac{2x}{2}=\frac{6}{2}$

$x=3$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=3,\:y=2$

Therefore, the coordinates that satisfy the equations will be: (3, 2)

Hence, option C is correct.