Question

find the point of intersection for
$y = 3x - 5$
$2x + y = 10$

Explanation:

Step1: Substitute y in the second - equation

Substitute \(y = 3x - 5\) into \(2x + y=10\). We get \(2x+(3x - 5)=10\).
\[2x + 3x-5=10\]

Step2: Simplify the left - hand side

Combine like terms: \(5x-5 = 10\).

Step3: Solve for x

Add 5 to both sides: \(5x=10 + 5\), so \(5x=15\). Then divide both sides by 5, \(x = 3\).

Step4: Solve for y

Substitute \(x = 3\) into \(y = 3x-5\). So \(y=3\times3 - 5=9 - 5 = 4\).

Answer:

\((3,4)\)