18. Systems of Equations and Matrices

Determinants and Cramer's Rule

18. Systems of Equations and 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 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, calculate the determinant of the coefficient matrix, which is |A| = (3)(7) - (1)(2).

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|.

4:36m

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Determinants and Cramer's Rule practice set

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Struggling with Precalculus?

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