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2 years ago

Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.

Mathematics

1 answer:

vaieri [72.5K]2 years ago

5 0

Answer:

try find apps about answering this question im not sure about this one :)

Step-by-step explanation:

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uysha [10]

Answer:

Add 1 to both sides.

Multiply both sides by -2.

Add 8 to both sides.

Divide both sides by 5.

Step-by-step explanation:

Step 1

$-\dfrac{1}{2}(5x-8)-1=6\quad \quad \textsf{Write the equation.}$

Step 2

$-\dfrac{1}{2}(5x-8)=7 \quad \quad \textsf{Add 1 to both sides.}$

This is called the Addition Property of Equality. When the same number is added to both sides of an equation, the two sides remain equal.

$\implies -\dfrac{1}{2}(5x-8)-1+1=6+1$

$\implies -\dfrac{1}{2}(5x-8)=7$

Step 3

$5x-8=-14 \quad \quad \textsf{Multiply both sides by -2.}$

This is called the Multiplication Property of Equality. When both sides of an equation are multiplied by the same number, the two sides remain equal.

$\implies -2 \cdot -\dfrac{1}{2}(5x-8)=-2 \cdot 7$

$\implies 5x-8=-14$

Step 4

$5x=-6 \quad \quad \textsf{Add 8 to both sides.}$

This is called the Addition Property of Equality. When the same number is added to both sides of an equation, the two sides remain equal.

$\implies 5x-8+8=-14+8$

$\implies 5x=-6$

Step 5

$x=-\dfrac{6}{5} \quad \quad \textsf{Divide both sides by 5.}$

This is called the Division Property of Equality. When both sides of an equation are divided by the same number, the two sides remain equal.

$\implies \dfrac{5x}{5}=\dfrac{-6}{5}$

$\implies x=\dfrac{-6}{5}$

Conclusion

$\begin{aligned}-\dfrac{1}{2}(5x-8)-1 & =6 & \quad \quad& \textsf{Write the equation.}\\\\-\dfrac{1}{2}(5x-8) & =7 & & \boxed{\textsf{Add 1 to both sides.}}\\\\5x-8 & =-14 & & \boxed{\textsf{Multiply both sides by -2.}}\\\\5x & =-6 & & \boxed{\textsf{Add 8 to both sides.}}\\\\x & =-\dfrac{6}{5} & & \boxed{\textsf{Divide both sides by 5.}}\\\end{aligned}$