Question

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
10x+5y=52.5
30x-7y=80.5

Answer 1

multiply the first by -3, add to the second

Answer 2

ok so 10x*-3

Answer 3

ok now is the second part or the whole thing

Answer 4

ok i messed up yet again so let me start afresh

Answer 5

ok great

Answer 6

here we go ready?

Answer 7

\[10x+5y=52.5\]
\[30x-7y=80.5\] multiply top by -3 get
\[-30x-15y=-157.5\]
\[30x-7y=80.5\]

Answer 8

add the two equations together. the x's add up to zero and you get one equation in y, namely
\[-22y=-77\]
solve for y and get
\[y=\frac{77}{22}=\frac{7}{2}=3.5\]

Answer 9

now that we know y, replace y by 3.5 in either equation and solve for x

Answer 10

\[10x+5y=52.5\]
\[10x+5\times 3.5=52.5\]
\[10x+17.5=52.5\]
\[10x=35\]
\[x=3.5\]

Answer 11

so both x and y are 3.5
it doesn't usually work out that way

Answer 12

ok got it now