Question

Solve the following systems of linear equations using substitution

4x - 2y = 20 and x - 4y = -16

Answer 1

The solution to this system of linear equations is (x, y) = (8, 6)

Explanation:

We can solve this system of linear equations using substitution. To start, we'll isolate one of the variables in one of the equations, then substitute that expression into the other equation.

Starting with the first equation, we'll isolate x:

4x - 2y = 20

4x = 20 + 2y

x = 5 + 0.5y

Next, we'll substitute this expression for x into the second equation:

x - 4y = -16

5 + 0.5y - 4y = -16

5 - 3.5y = -16

Adding 3.5y to both sides:

5 = 3.5y - 16

Adding 16 to both sides:

21 = 3.5y

Finally, dividing both sides by 3.5:

y = 6

So, the value of y is 6. To find x, we can substitute this value back into the expression we found earlier:

x = 5 + 0.5y

x = 5 + 0.5(6)

x = 5 + 3

x = 8

So, the solution to this system of linear equations is (x, y) = (8, 6).

Answer 2

(8, 6)

Explanation:

Given system of linear equations:

`\begin{cases}4x - 2y = 20 \\x - 4y = -16\end{cases}`

Rearrange the second equation to isolate x:

`\implies x=4y-16`

Substitute the found expression for x into the first equation and solve for y:

`\implies 4(4y-16)-2y=20`

`\implies 16y-64-2y=20`

`\implies 14y-64=20`

`\implies 14y=84`

`\implies y=6`

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

`\implies x=4(6)-16`

`\implies x=24-16`

`\implies x=8`

Therefore, the solution to the given system of linear equations is (8, 6).