Question

find the point of intersection for each system.y=2x-3 x+y=15

Answer 1

Answer:

$(6,9)$

Explanation:

Here, we want to get the point of intersection of the two lines

Mathematically, we can solve the system of linear equations simultaneously.

The solution to the system will represent the point of intersection

From what we have, we can directly substitute equation i into ii

We have that as:

$\begin{gathered} x\text{ + 2x-3 = 15} \\ 3x-3\text{ = 15} \\ 3x\text{ = 15 + 3} \\ 3x\text{ = 18} \\ x\text{ = }\frac{18}{3} \\ x\text{ = 6} \end{gathered}$

Recall:

$\begin{gathered} y\text{ = 2x-3} \\ substitute\text{ the x value into the above} \\ y\text{ = 2\lparen6\rparen -3} \\ y\text{ = 12-3} \\ y\text{ = 9} \end{gathered}$

The point of intersection is thus (6,9)