Question

Find the solution to 5x=2x+3
On graph there are two lines crossing at (1,5) other points are (0,0),(2,2)

Answer 1

To solve the equation \(5x = 2x + 3\), we can start by isolating \(x\).

1. Subtract \(2x\) from both sides:
\[
5x - 2x = 3
\]
This simplifies to:
\[
3x = 3
\]

2. Next, divide both sides by 3:
\[
x = 1
\]

Now that we have found \(x = 1\), we can substitute this value back into either side of the original equation to find \(y\):

Substituting \(x = 1\) into the \(y = 5x\) equation:
\[
y = 5(1) = 5
\]

So, the solution to the equation is the point \( (1, 5) \).

### Graph Interpretation

You mentioned there are two lines crossing at \((1, 5)\). Let’s confirm that:

1. The first line, represented by \(y = 5x\), goes through the points:
- When \(x = 0\), \(y = 0\) (point: \((0, 0)\)).
- When \(x = 2\), \(y = 10\) (not listed in your points).

2. The second line can be derived from the other side of the original equation, \(y = 2x + 3\):
- When \(x = 0\), \(y = 3\) (point: \((0, 3)\)).
- When \(x = 1\), \(y = 5\) (point: \((1, 5)\) as you noted).
- When \(x = 2\), \(y = 7\) (point: \((2, 7)\)).

### Conclusion

The two lines \(y = 5x\) and \(y = 2x + 3\) indeed intersect at the point \((1, 5)\). Your points on the graph \((0, 0)\) and \((2, 2)\) suggest possible other plot points, but \((2, 2)\) does not belong to either of the original equations. The correct points specifically related to the two equations are as explained above.

So, the final solution is:
\[
\text{Intersection point: } (1, 5)
\]