Q 28 - Intermediate Algebra

Question

Without graphing, determine the number of solutions and then classify the system of equations.

$$\begin{gathered} y=-\frac{1}{2}x+5 \\ x+2y=10 \end{gathered}$$

Step-by-Step Solution

Answer

The number of solution is infinite and the system of equations is coincident lines, consistent and dependent. 

Step 1. Given information

The system of equations is $\left\{\begin{array}{l}y=-\frac{1}{2}x+5\\ x+2y=10\end{array}\right.$

Step 2. Solve the first equation for y and find the slope and y -intercept.

$y=-\frac{1}{2}x+5$

Here the slope is $-\frac{1}{2}$

And the $y$-intercept is $5$

Step 3. Solve the second equation for y and find the slope and y -intercept.

$$\begin{gathered} x+2y=10 \\ 2y=10-x \\ y=-\frac{1}{2}x+5 \end{gathered}$$

Here the slope is $-\frac{1}{2}$

And the $y$-intercept is $5$

Step 4. Required answer

Here the slopes and $y$-intercepts are same.

Therefore, the system of equation is coincident lines with infinite solution and is consistent and dependent.