Question

{2x+2y=2,2(x+y)=10}A. single solution B. no solution C. infinite solutions

Answer 1

To find the number of solutions of a system of linear equations you need to identify the slope (m) in each equation:

$y=mx+b$

-If the slope is the same in both lines the system has no solution

-If the slope is different in the lines the system has one solution

-If the equation are the same (incluided the value of b) the system has infinitely many solutions

You have the next equations:

$\begin{gathered} 2x+2y=2 \\ 2(x+y)=10 \end{gathered}$

Write the equations in slope-intercept form y=mx+b (solve for y).

First equation:

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

Second equation:

$\begin{gathered} 2x+2y=10 \\ 2y=-2x+10 \\ y=-\frac{2}{2}x+\frac{10}{2} \\ \\ y=-x+5 \end{gathered}$As the equations have the same slope m = -1, the system has no solution (the line doesn't cross each other)