Question

Question #95527

Answer 1

`{(x = -3), (y = -4) :}`

Explanation:

Start by dividing both sides of the second equation by `-2`. You will end up with

`(2y)/(-2) = 7/-2 + (5x)/-2`

`-y = -7/2 - (5x)/2`

Now, notice that the left-hand side of the two equations is equal.

`{( -y = -5/7 - (11x)/7), (-y = -7/2 - (5x)/2) :}`

This means that you can equate the two right-hand sides to get an equation with one unknown, `x`.

`-5/7 - (11x)/7 = -7/2 - (5x)/2`

DIvide or multiply both sides by `-1` to get rid of the minus signs.

`5/7 + (11x)/7 = 7/2 + (5x)/2`

`(5 + 11x)/7 = (7 + 5x)/2`

Next, cross multiply, i.e. multiply the numerator of one fraction by the denominator of the second fraction and vice versa. You will end up with

`7 * (7 + 5x) = 2 * (5 + 11x)`

This will be equivalent o

`49 + 35x = 10 + 22x`

Subtract `22x` and `49` from both sides to get

`13x = - 39`

Finally, divide both sides by `13` to isolate `x`

`x = -39/13 = -3`

Now that you have a value for `x`, pick one of the two equations and use it to find the value of `y`.

`2y = 7 + 5 * (-3)`

`2y = -8`

Divide both sides by `2` to isolate `y`

`y = -4`

Therefore, your system of two equations with two unknowns has the solution set

`{(x = -3), (y = -4) :}`

If you want, you can double-check the result by plugging in the two values into the original equations.

You will have

`-(-4) = -5/7 - (11 * (-3))/7`

`4 = (-5 + 33)/7" "color(green)(sqrt())`

and

`2 * (-4) = 7 + 5 * (-3)`

`-8 = 7 - 15" "color(green)(sqrt())`