7. Systems of Equations & Matrices

Determinants and Cramer's Rule

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

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Multiple Choice

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

$x = 1, y = 1$

$x = - 1, y = 1$

$x = 1, y = - 1$

$x = - 1, y = - 1$

Verified step by step guidance

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.

For the second equation -2x = 7y - 9, rearrange it to standard form by moving all terms to one side: 2x + 7y = 9.

Now, you have the system of equations in standard form: 3x + y = 4 and 2x + 7y = 9.

To use Cramer's Rule, first find the determinant of the coefficient matrix, D. The matrix is [[3, 1], [2, 7]], so D = (3)(7) - (1)(2).

Next, find the determinants for Dx and Dy by replacing the respective columns with the constants from the equations. Solve for x and y using x = Dx/D and y = Dy/D.

4:36m

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Determinants and Cramer's Rule practice set

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Go to Practice

Struggling with College Algebra?

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

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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.
$y=-3x+4$
$-2x=7y-9$