Question

$\Large{\underline{\underline{\tt{\red{\bf{Question}}}}}}$

★ Solve This Equation by Matrix Method.

↪2x - 8y = 9
↪3x + 5y = 5

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Answer 1

$\color{red}\huge{\underline{\underline{GIVEN\dag}}}$

• $2x - 8y = 9$
• $3x + 5y = 5$

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

We know that;

${ \boxed{ \color{blue}\frac{x}{c _{1}b _{2} -c _{2}b _{1} } = \frac{ - y}{a_{2}c_{1} - a_ {1}c _{2}} = \frac{1}{a_{2}b_{1} - a_{1}b_{2}}}}$

Where;

a,b & c are the coefficients of the equation.

$ax+by+c=0$

$\implies 2x-8y-9=0.......(1)$

$\implies 3x+5y-5=0.......(2)$

Here,

• $a_{1}=2$
• $a_{2}=3$
• $b_{1}=-8$
• $b_{2}=5$
• $c_{1}=-9$
• $c_{2}=-5$

$\implies \frac{x}{-45 + 40} = \frac{ - y}{-27 + 10} = \frac{1}{24 - 10}$

$\implies \frac{x}{ -5} = \frac{ - y}{- 17} =\frac{1}{ 14}$

$\implies \frac{x}{-5} = \frac{1}{14}$

${\boxed{ \color{orange} \therefore \: x =\frac{-5}{14}}}$

$\implies\frac{ - y }{-17}= \frac{1}{ 14}$

${\boxed{\color{orange} \therefore \: y =\frac{17}{14}}}$

HOPE THAT HELPS!!!

Answer 2

Step-by-step explanation:

The augmented matrix is -1 1 -1

3 -5 7

Multiply the first row by -1: 1 -1 1

3 -5 7

Add -3(row 1) to row 2 and replace row 2 with the result:

1 -1 1

0 -2 4

Divide row 2 by -2: 1 -1 1

0 1 -2

Add row 2 to row 1 and replace row 1 by the result:

1 0 -1

0 1 -2

Restore variables: 1x + 0y = -1

0x + 1y = -2

So, x = -1 and y = -2