Write each equation in standard form and use Cramer's Rule to solve the system.
$y-9x=-3$
$-3x=4y-1$

$y=3,x=0$

$x=0,y=3$

$x=-$\frac$13,y=1$

$x=$\frac$13,y=0$

Verified step by step guidance

First, rewrite each equation in standard form, which is Ax + By = C. For the first equation y - 9x = -3, rearrange it to 9x - y = 3.

For the second equation -3x = 4y - 1, rearrange it to 3x - 4y = 1.

Now, you have the system of equations in standard form: 9x - y = 3 and 3x - 4y = 1.

To use Cramer's Rule, calculate the determinant of the coefficient matrix, which is formed by the coefficients of x and y: D = | 9 -1 | | 3 -4 |. Compute D = (9)(-4) - (-1)(3).

Next, calculate the determinants for Dx and Dy. For Dx, replace the x-coefficients with the constants from the right side of the equations: Dx = | 3 -1 | | 1 -4 |. For Dy, replace the y-coefficients: Dy = | 9 3 | | 3 1 |. Compute Dx and Dy using the same determinant formula.

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Write each equation in standard form and use Cramer's Rule to solve the system.y−9x=−3y-9x=-3y−9x=−3−3x=4y−1-3x=4y-1−3x=4y−1

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Determinants and Cramer's Rule practice set

Write each equation in standard form and use Cramer's Rule to solve the system.
$y-9x=-3$
$-3x=4y-1$