## anonymous 4 years ago 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

1. anonymous

multiply the first by -3, add to the second

2. anonymous

ok so 10x*-3

3. anonymous

ok now is the second part or the whole thing

4. anonymous

ok i messed up yet again so let me start afresh

5. anonymous

ok great

6. anonymous

7. anonymous

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

8. anonymous

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 $y=\frac{77}{22}=\frac{7}{2}=3.5$

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

ok got it now