Write each equation in standard form and use Cramer's Rule to solve the system.
$y=-3x+4$
$-2x=7y-9$

• A. $x=1,y=1$
• B. $x=-1,y=1$
• C. $x=1,y=-1$
• D. $x=-1,y=-1$

Answer: (A)

Verified step by step guidance

1. First, rewrite each equation in standard form, which is Ax + By = C. For the first equation y = -3x + 4, rearrange it to 3x + y = 4.
2. For the second equation -2x = 7y - 9, rearrange it to 2x + 7y = 9.
3. Now, you have the system of equations in standard form: 3x + y = 4 and 2x + 7y = 9.
4. To use Cramer's Rule, calculate the determinant of the coefficient matrix, which is |A| = (3)(7) - (1)(2).
5. Next, calculate the determinants for x and y using the matrices formed by replacing the respective columns with the constants from the right-hand side of the equations, and solve for x and y using Cramer's Rule: x = Dx/|A| and y = Dy/|A|.