Question

a system of linear equations y= 2x+5 and y=x+2 which ordered pair is a solution to the equations?

Answer 1

To find the ordered pair that is a solution to both equations \( y = 2x + 5 \) and \( y = x + 2 \), we can set the two equations equal to each other since they both equal \( y \).

1. Set the equations equal:
\[
2x + 5 = x + 2
\]

2. Solve for \( x \):
\[
2x - x = 2 - 5
\]
\[
x = -3
\]

3. Substitute \( x = -3 \) back into one of the original equations to find \( y \). We can use \( y = x + 2 \):
\[
y = -3 + 2 = -1
\]

Thus, the ordered pair that is a solution to both equations is \( (-3, -1) \).

You can also verify this by plugging \( x = -3 \) back into the other equation \( y = 2x + 5 \):
\[
y = 2(-3) + 5 = -6 + 5 = -1
\]

Both equations give the same \( y \)-value when \( x = -3 \), confirming the solution is correct.

So the solution is:
\[
\text{Ordered pair: } (-3, -1)
\]