Question

If `2x+6y=2` and `-7+5y=x`, what is `2x`?

Answer 1

2x=-4

Explanation:

You can solve this by using a system of equations and the substitution method.

`2x+6y=2`
`-7+5y=x`

Since the second equation has an `x=`, substitute it for the `x` in the first equation.

`2(-7+5y)+6y=2`

Solve for `y` like you would any other equation.

`-14+10y+6y=2`
`16y=16`
`y=1`

Finally, plug your new `y` value into either of the original equations and solve. Here, I used the second one.

`-7+5(1)=x`
`x=-2`

Multiply this `x` value by 2 to find 2x.

`2x=2(-2)=-4`

Hope this helps!

Answer 2

`2x=-4`

Explanation:

`2x+6y=2to(1)`

`-7+5y=xto(2)`

`"substitute "x=-7+5y" into equation "(1)`

`2(-7+5y)+6y=2`

`rArr-14+10y+6y=2`

`rArr-14+16y=2`

`"add 14 to both sides"`

`cancel(-14)cancel(+14)+16y=2+14`

`rArr16y=16`

`"divide both sides by 16"`

`(cancel(16) y)/cancel(16)=16/16`

`rArry=1`

`"substitute "y=1" into equation "(2)`

`-7+5=xrArrx=-2`

`rArr2x=2xx-2=-4`

Answer 3

`color(blue)(2x = (-4)`

Explanation:

Given:

`color(blue)(2x+6y=2)` `color(red)(Equation.1)`

`color(blue)(-7+5y=x)` `color(red)(Equation.2)`

`color(green)(Step-1)`

We can write `color(red)(Equation.2)` as

`-7+5y=x`

Add `color(green)(+7` on both side of the equation:

`-7+5y color(green)(+7=x color(green)(+7`

`-cancel 7+5y color(green)(+ cancel 7=x color(green)(+7`

`5y =x +7`

Add `color(brown)((-x)` on both side of the equation:

`5y+ color(brown)(-x) =x +7+color(brown)(-x)`

`5y+ color(brown)(-x) =cancel x +7+color(brown)(- cancel x)`

`5y -x =7`

`color(blue)(-x + 5y =7` `color(red)(Equation.3)`

`color(green)(Step-2)`

Consider:

`color(blue)(2x+6y=2)` `color(red)(Equation.1)`

`color(blue)(-x + 5y =7` `color(red)(Equation.3)`

Multiply each term in `color(red)(Equation.3)` by `2` to get

`color(blue)(-2x + 10y =14` `color(red)(Equation.4)`

Add `color(red)(Equation.1)` and `color(red)(Equation.4)`

`color(blue)(2x+6y=2)` `color(red)(Equation.1)`

`color(blue)(-2x + 10y =14` `color(red)(Equation.4)` to get

`16y=16`

Divide each term by `16`

`(16y)/16=16/16`

`(cancel 16*y)/ cancel 16=16/16`

Hence,

`color(blue)(y= 1`

`color(green)(Step-3)`

Substitute `color(blue)(y= 1` in

`color(blue)(2x+6y=2)` `color(red)(Equation.1)`

`2x+6*1 =2`

`2x+6 =2`

Add `(-6)` to both sides

`2x+6 +(-6) =2 + (-6)`

`2x+cancel 6 +(-cancel 6) =2 + (-6)`

`2x=-4`

Divide both sides by `2`

`(2x)/2=(-4)/2`

`(cancel 2x)/cancel 2=(-4)/2`

`color(blue)(x=(-2)`

So, we have

`color(blue)(x=(-2)`

`color(blue)(y= 1`

You want to find the value of `color(brown)(2x`

`color(blue)(2x = 2*(-2) = -4)`

Hence

`color(blue)(2x = (-4)`

Hope this helps.