Question

Use Cramer's rule to find the solution to the following system of linear equations.

x-2y = -7
5x-9y=-5​

Answer 1

x - 2y = -7

5x - 9y = -5​

`D=\left|\, 1\quad-2\atop5\quad-9\right|=1\cdot(-9)-(-2)\cdot5=-9+10=1\\\\\\x=\frac\left1=-7(-9)-(-2)(-5)=63-10=53\\\\\\y=\frac\, 1\quad-7\atop5\quad-5\right1=1\cdot(-5)-(-7)\cdot5=-5+35=30`

Answer 2

x = 53

y = 30

Explanation:

Step(I):-

Given equations are

x -2y =-7 ...(I)

5x-9y =-5 ..(ii)

The matrix form AX = B

`\left[\begin{array}{ccc}1&-2\\ 5 & -9\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}-7\\-5\\\end{array}\right]`

The determinant

`= \left|\begin{array}{ccc}1&-2\\5&-9\\\end{array}\right| = -9+10 =1`

By using Cramer's Rule

Δ₁ =
`\left[\begin{array}{ccc}-7&-2\\\\-5&-9\end{array}\right]`



The determinant is Δ₁ = -9 X -7 - (10 ) = 53

x = Δ₁ / Δ

x = 53

The determinant

Δ₂ =



Δ₂ = -5 +35



y = Δ₂/Δ = 30