Q1. - Algebra 2

Question

Explain why a system of linear equations cannot have exactly two solutions.

Step-by-Step Solution

Answer

The highest degree of the equation is 1 so exactly two solutions are not possible.

Step-1 – Degree of an equation

The highest power of the variable in the equation is the degree of the equation.

For a system of equation with highest degree as 1 can have either one solution, no solution or infinite solutions.

For a system of equation with highest degree as 2 can have two solution, no solution or infinite solutions.

Step-2 –System of Equations of degree one

For example: Consider system of equations:

$\begin{array}{c}y=2x+9\\ y=x+3\end{array}$

Consider the first equation $y=2x+9$.

The equation is in the form $y=mx+c$. Here slope m of the line is 2 and intercept of y-axis c is 9.

Now, consider the second equation $y=x+3$. The equation is in the form $y=mx+c$. Here slope m of the line is 1 and intercept of y-axis c is 3.

Step-3 – Identify the point of intersection of the equations

Plot the equations on the same plane and the point where both the equations intersect is the solution of the system of the equations.

The red line denotes the equation $y=2x+9$ and blue line denotes the equation $y=x+3$.

Therefore, the point of intersection is $\left(-6,-3\right)$.

Hence, only solution is possible and not two solutions.