Question

tell whether the ordered pair is a solution to the equation. show all steps!!!

1. $4x + 2y = 24$ $(-2,16)$
2. $4x - 2y = -32$ $(5,-24)$
3. $-x + 3y = 18$ $(-5,4)$
4. $4x - 2y + 2 = 24$ $(0,13)$
5. $4 + 2y = -5x$ $(3,-9)$
6. $4 = 2y - 7x$ $(6,19)$
7. $12 - 4x = 7y$ $(3,0)$
8. $4y - 6 = 3x$ $(8,8)$

Explanation:

Let's solve problem 1: Determine if \((-2, 16)\) is a solution to \(4x + 2y = 24\)

Step 1: Identify \(x\) and \(y\) values

From the ordered pair \((-2, 16)\), we have \(x = -2\) and \(y = 16\).

Step 2: Substitute into the equation

Substitute \(x = -2\) and \(y = 16\) into the left - hand side of the equation \(4x+2y\):
\[

$$\begin{align*} 4x + 2y&=4\times(-2)+2\times16\\ &=-8 + 32\\ &= 24 \end{align*}$$

\]

Step 3: Compare with the right - hand side

The right - hand side of the equation \(4x + 2y = 24\) is \(24\). Since the left - hand side (\(24\)) is equal to the right - hand side (\(24\)) after substitution.

Step 1: Identify \(x\) and \(y\) values

From the ordered pair \((5,-24)\), we have \(x = 5\) and \(y=-24\).

Step 2: Substitute into the equation

Substitute \(x = 5\) and \(y = - 24\) into the left - hand side of the equation \(4x-2y\):
\[

$$\begin{align*} 4x-2y&=4\times5-2\times(-24)\\ &=20 + 48\\ &=68 \end{align*}$$

\]

Step 3: Compare with the right - hand side

The right - hand side of the equation \(4x - 2y=-32\) is \(-32\). Since \(68
eq - 32\).

Step 1: Identify \(x\) and \(y\) values

From the ordered pair \((-5,4)\), we have \(x=-5\) and \(y = 4\).

Step 2: Substitute into the equation

Substitute \(x=-5\) and \(y = 4\) into the left - hand side of the equation \(-x + 3y\):
\[

$$\begin{align*} -x+3y&=-(-5)+3\times4\\ &=5 + 12\\ &=17 \end{align*}$$

\]

Step 3: Compare with the right - hand side

The right - hand side of the equation \(-x + 3y = 18\) is \(18\). Since \(17
eq18\).

Answer:

The ordered pair \((-2,16)\) is a solution to the equation \(4x + 2y=24\)

Let's solve problem 2: Determine if \((5,-24)\) is a solution to \(4x-2y=-32\)