Question

Find the point of intersection for the following two lines: $\left\{\begin{array}{l}x+y=5\\ 3x+y=1\end{array}\right.$

Answer 1

Find the point of intersection:

The equation of the given lines are $x+y=5$ and $3x+y=1$.

The point of intersection of the two lines can be obtained by the method of substitution.

The substitution method involves substituting one equation into the other, thus eliminating to one variable.

Isolate the variable x in the equation $x+y=5$ to get the value of x.

$x=5-y$

Substitute the obtained value of x in the equation $3x+y=1$.

$$\begin{gathered} 3(5-y)+y=1 \\ \Rightarrow 15-3y+y=1 \\ \Rightarrow 15-2y=1 \\ \Rightarrow -2y=1-15 \\ \Rightarrow -2y=-14 \\ \Rightarrow 2y=14 \\ \Rightarrow y=\frac{14}{2} \\ \Rightarrow y=7 \end{gathered}$$

Now substitute the obtained value of $y$ as $7$ in the equation $x=5-y$ to get the value of $x$.

$$\begin{gathered} x=5-7 \\ x=-2 \end{gathered}$$

Hence, the required point of intersection is $(-2,7)$