Question

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Answer 1

Answer:

• (- 5, 9)

Step-by-step explanation:

Given system of equations

• - 2x - y = 1
• - 4x - y = 11

Express the first equation as

• y = - 2x - 1

Substitute the value of y into second equation

• - 4x - (- 2x - 1) = 11

Solve for x

• - 4x + 2x + 1 = 11
• - 2x + 1 = 11
• - 2x = 10
• 2x = - 10
• x = - 5

Find the value of y

• y = - 2(- 5) - 1 = 10 - 1 = 9

Answer 2

Answer:

(-5, 9)

Step-by-step explanation:

Given system of linear equations:

$\begin{cases}-2x-y=1\\-4x-y=11\end{cases}$

To solve by substitution, use arithmetic operations to isolate y in Equation 1:

$\implies -2x-y=1$

$\implies -2x-y+y=1+y$

$\implies -2x=1+y$

$\implies -2x-1=1+y-1$

$\implies y=-2x-1$

Substitute the expression for y into Equation 2 and solve for x:

$\implies -4x-(-2x-1)=11$

$\implies -4x+2x+1=11$

$\implies -2x+1=11$

$\implies -2x+1-1=11-1$

$\implies -2x=10$

$\implies -2x \div -2=10 \div -2$

$\implies x=-5$

Substitute the found value of x into one of the equations and solve for y:

$\implies -2(-5)-y=1$

$\implies 10-y=1$

$\implies 10-y+y=1+y$

$\implies 10=1+y$

$\implies 10-1=1+y-1$

$\implies y=9$

Therefore, the solution to the given system of linear equations is (-5, 9).

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