# 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?

Mar 26, 2018

$\left(3 , 2\right)$ 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?
$y = - x + 5 \mathmr{and} x - 2 y = - 4$ & $x = 3 , y = 2 :$

Is $3 - 2 \times 2 = - 4$ ?
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

Mar 26, 2018

See Below.

#### Explanation:

In an ordered pair $\left(x , y\right)$; 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, $\left(3 , 2\right)$ as an ordered pair.

And, The Equations:

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

$x - 2 y = - 4$...........................(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 $\left(3 , 2\right)$ isn't a solution for this system of simultaneous equations.

Hope this helps.

Mar 26, 2018

$\left(3 , 2\right)$ is not the solution.

The solution is $\left(2 , 3\right)$.

#### Explanation:

$\text{Equation 1} :$ $y = - x + 5$

$\text{Equation 2} :$ $x - 2 y = - 4$

Since Equation 1 is already solved for $y$, substitute $\textcolor{red}{- x + 5}$ for $y$ in Equation 2 and solve for $x$.

$x - 2 \left(\textcolor{red}{- x + 5}\right) = - 4$

Expand.

$x + 2 x - 10 = - 4$

Simplify.

$3 x - 10 = - 4$

Add $10$ to both sides.

$3 x = - 4 + 10$

Simplify.

$3 x = 6$

Divide both sides by $3$.

$x = \frac{6}{3}$

color(blue)(x=2

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

$y = - \textcolor{b l u e}{2} + 5$

color(green)(y=3

The solution is $\left(2 , 3\right)$, therefore $\left(3 , 2\right)$ is not the solution.

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