Question

Which ordered pair is a solution of 3y+2=2x-5

Answer 1

To find an ordered pair \((x, y)\) that is a solution to the equation \(3y + 2 = 2x - 5\), we can rearrange the equation and solve for \(y\) in terms of \(x\):

1. Start with the equation:
\[
3y + 2 = 2x - 5
\]

2. Subtract 2 from both sides:
\[
3y = 2x - 5 - 2
\]
\[
3y = 2x - 7
\]

3. Divide everything by 3 to isolate \(y\):
\[
y = \frac{2}{3}x - \frac{7}{3}
\]

Now we have \(y\) expressed in terms of \(x\). To find an ordered pair, we can choose any value for \(x\) and compute \(y\).

For example, let’s choose \(x = 0\):
\[
y = \frac{2}{3}(0) - \frac{7}{3} = -\frac{7}{3}
\]
This gives us the ordered pair \((0, -\frac{7}{3})\).

Now let’s verify if this pair satisfies the original equation:
\[
3y + 2 = 2x - 5
\]
Substituting \(x = 0\) and \(y = -\frac{7}{3}\):
\[
3(-\frac{7}{3}) + 2 = 2(0) - 5
\]
\[
-7 + 2 = -5
\]
\[
-5 = -5
\]
This is a true statement.

Thus, the ordered pair \((0, -\frac{7}{3})\) is indeed a solution of the equation \(3y + 2 = 2x - 5\).

You can find other pairs by choosing different values for \(x\) and calculating \(y\) accordingly.