Question

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
2x + 10y = 58
-14x + 8y = 140

Answer 1

multiply first equation by 7 and add

Answer 2

14x+70y=406

Answer 3

adding these will eliminate x and give an equation in y only
solve this and plug this value into first equationm to find vaue of y

Answer 4

so it takes out 14x

Answer 5

so 70y+8y=140

Answer 6

\[\left[\begin{matrix}2 & 10\\ -14 & 8\end{matrix}\right]= \left(\begin{matrix}58 \\ 140\end{matrix}\right)\]

time row 1 by 7: ( 14 70 = 406)
add the modified row 1 to 2:
0x+78y=546)

now
\[\left[\begin{matrix}14 & 70\\ 0 & 78\end{matrix}\right]= \left(\begin{matrix}406 \\ 546\end{matrix}\right)\]

then y=546/78=7
and x=(406-(70*7))/14=-6

UNIQUE SOLUTION, a square matrix A will alway result in an equation A(x,y)=(a,b) with a unique solution UNLESS the rows of A are multiple of one another

Answer 7

Simply put, check if the coefficients of x and y in eq 1are multiples of those in equation 2