Given two lines y=2x+1 and 3x - y =5 find the intersection poin of the two line
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Substitute the expression for $y$ from the first equation into the second equation.
Given:
1) $y = 2x + 1$
2) $3x - y = 5$
Substitute (1) into (2):
$$3x - (2x + 1) = 5$$
Step 2: Solve for $x$.
$$3x - 2x - 1 = 5$$
$$x - 1 = 5$$
$$x = 5 + 1$$
$$x = 6$$
Step 3: Substitute the value of $x$ back into the first equation to find $y$.
$$y = 2(6) + 1$$
$$y = 12 + 1$$
$$y = 13$$
The intersection point is $\boxed{(6, 13)}$.
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