Question

How do you substitute to determine if the ordered pair (3, 2) is a solution of the system of equations y=-x+5 and x-2y=-4?

Answer 1

`(3, 2)` isn't a solution of the system of equations.

Explanation:

You substitute the new thing for the old thing,
and you replace the old thing with or by the new thing.

Substitute 3 for x and 2 for y, and check if both equations are correct?
`y=-x+5 and x-2y=-4` & `x = 3, y = 2:`

Is `3 -2 xx2 = -4` ?
Is `-1 = -4`? No!!

Is this true `2 = -3 + 5`?
`2 = 2` , it's true

(3,2) lies on one the line but not both, and it is not the not a solution of the system of equations.

https://www.desmos.com/calculator/hw8eotboqh

Answer 2

See Below.

Explanation:

In an ordered pair `(x,y)`; The first term is the value for the first

variable and the second term is the value for the second variable in

a system of simultaneous equations.

So, Here, We have, `(3,2)` as an ordered pair.

And, The Equations:

`y = -x + 5`..........................(i)

`x - 2y = -4`...........................(ii)

Let's substitute `x = 3` and `y = 2` in the equations eq(i) and eq(ii).

For (i):

`2 = -3 + 5` Which is correct, So The ordered pair satisfies this equation.

For (ii):

`3 - 4 = -4` Which is not possible, So, The ordered pair does not satisfy the equation.

So, The ordered pair `(3,2)` isn't a solution for this system of simultaneous equations.

Hope this helps.

Answer 3

`(3,2)` is not the solution.

The solution is `(2,3)`.

Explanation:

`"Equation 1":` `y=-x+5`

`"Equation 2":` `x-2y=-4`

Since Equation 1 is already solved for `y`, substitute `color(red)(-x+5)` for `y` in Equation 2 and solve for `x`.

`x-2(color(red)(-x+5))=-4`

Expand.

`x+2x-10=-4`

Simplify.

`3x-10=-4`

Add `10` to both sides.

`3x=-4+10`

Simplify.

`3x=6`

Divide both sides by `3`.

`x=6/3`

`color(blue)(x=2`

Now substitute `color(blue)(2` for `x` in Equation 1 and solve for `y`.

`y=-color(blue)(2)+5`

`color(green)(y=3`

The solution is `(2,3)`, therefore `(3,2)` is not the solution.

graph{(y+x-5)(x-2y+4)=0 [-10, 10, -5, 5]}