How do you solve the system of equations $2 x + 8 y = 6$ $2x+8y=6$ and $- 5 x - 20 y = - 15$ $-5x-20y=-15$ ?

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How do you solve the system of equations $2 x + 8 y = 6$ $2x+8y=6$ and $- 5 x - 20 y = - 15$ $-5x-20y=-15$ ?

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Answer 1 · 2016-11-19T21:21:14

This system of equation doesn't have any solutions.

Explanation:

$2 x + 8 y = 6$ $2x+8y=6$
$- 5 x - 20 y = - 15$ $-5x-20y=-15$

Let's simplify these equations: divide the first one by $2$ $2$ andd the second by $- 5$ $-5$ :

$x + 4 y = 3$ $x+4y=3$
$x + 4 y = 15$ $x+4y=15$

Now, using any of the equations, we must express one variable by the other, let's say $x$ $x$ by $y$ $y$ from the second equation:

$x = 15 - 4 y$ $x=15-4y$

Using this we solve the other equation:

$x + 4 y = 3$ $x+4y=3$
$15 - 4 y + 4 y = 3$ $15-4y+4y=3$
$15 = 3$ $15=3$

We got $15 = 3$ $15=3$ which obviously isn't true so this equation has no solution. It follows that this system of equation doesn't have any solutions as well.

Answer 2 · 2016-11-19T21:24:14

$x$ $x$ can have any value and the equations will work.
The y- values will depend on the x chosen.

Explanation:

$2 x + 8 y = 6 and - 5 x - 20 y = - 15$ $2x+8y =6" and "-5x -20y = -15$

There are different options available to solve the equations.
$\to$ $rarr" "$ elimination
$\to$ $rarr" "$ substitution $\to$ $rarr$ single variable
$\to$ $rarr" "$ equating
$\to$ $rarr" "$ matrices
$\to$ $rarr" "$ graphically

To be able to use substitution, a single variable in one of the equations is a useful indicator

$2 x + 8 y = 6 \div 2 \to x + 4 y = 3$ $2x+8y =6 " "div2 rarr " "x+4y=3$

Make x the subject of the equation:

$x = 3 - 4 y$ $color(red)(x = 3-4y)$

Replace $x$ $color(red)x$ in the second equation by $(3 - 4 y)$ $color(red)((3-4y))$

$- 5 x - 20 y = - 15$ $" "-5color(red)(x) -20y = -15$
$\times \times ↓$ $color(white)(xxxx)darr$
$- 5 (3 - 4 y) - 20 y = - 15$ $-5color(red)((3-4y))-20y =-15$

$- 15 + 20 y - 20 y = - 15$ $-15+20y -20y = -15$

$- 15 = - 15$ $-15 = -15$

$x$ $x$ can have any value

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How do you solve the system of equations $2 x + 8 y = 6$ $2x+8y=6$ and $- 5 x - 20 y = - 15$ $-5x-20y=-15$ ?

2 Answers

Explanation:

Explanation:

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How do you solve the system of equations $2 x + 8 y = 6$ $2x+8y=6$ and $- 5 x - 20 y = - 15$ $-5x-20y=-15$ ?