Emily W. answered • 11/27/21
High School and College Level Math and Science in Central Florida
12y = 17 - 9x
-4y - 3x = 31
I have spaced out the equation so you can see where the equal signs line up. After lining it up, I can see that there are y’s lined up -> this means we can find equal but opposite common multiple where both 12y and -4y meet so that we can eliminate them when we add them together. We want the y’s to have the same number on them but opposite signs.
where 12 and 4 meet: count by 12’s and count by 4’s
12 24 36 48 60
4 8 12 16 20 24
We can see that 4 and 12 meet at 12 because it’s the first number they both share in their lists.
12* 1 = 12 —> the whole top equation is multiplied by *1 to reach 12 (it stays the way it is)
4 * 3 = 12 —> the whole bottom equation is multiplied by 3 to reach 12
12y = 17 - 9x now everything in the second equation will be multiplied by 3
-4y * 3 - 3x * 3 = 31 * 3
rewrite
12y = 17 - 9x
-12y - 9x = 93
The y’s are equal and opposite = eliminate them! Everything leftover from both equations on the left side adds together and everything leftover on the right side adds together
-9x = 17 - 9x + 93
Now we solve algebraically for x
Combine 17+93
-9x = 110 - 9x add 9x to both sides
When we add 9x to both sides, both of the -9x terms disappear and there is nothing (zero) left on the left side
0 = 110
The statement we are left with is untrue because 0 is never equal to 110. This means there are no solutions to this equation. They are parallel lines that never intersect with each other.
Answer = no solution
Mark M.
If the equations had been put into standard form the inconsistency would be obvious.11/28/21