Jay H. answered • 02/24/14

Patient, Proven & Creative Approaches to Lifelong Learning

4X + 5Y = 30

5X - 6X = 36

5X - 6X = 36

Step One... combine like terms in the second equation:

5X - 6X = 36

5X - 6X = 36

-1x = 36

Step Two... set up this equation for elimination by multiplying / dividing to get the opposite of 4x. In other words, what do we need to do to -1x to change it into -4x? In this case multiply by 4. Since we multiply one side by 4 we need to do it to the other side to keep things equal:

-1x = 36

4(-1x) = (4)36

-4x = 144

Step Three... now we can see there is a -4x in the equation we've worked on, and a +4x in the first equation. Adding them both up will cancel out (or eliminate) the x component:

4X + 5Y = 30

-4x = 144

-4x = 144

0x + 5y = 444 we get 5y = 444

Step Four... solve for y. Do this by dividing both sides of the equation by 5:

(5y)/5 = (444)/5

y = 88.8

Step Five... plug in 88.8 into the original first equation to solve for x:

4X + 5Y = 30

4x + 5(88.8) = 30

4x + 5(88.8) = 30

4x + 444 = 30

4x +444 -444 = 30 -444

4x = -414

4x/4 = -414/4

x= -103.5

Finally we arrive at x=-103.5 and y=88.8. What this means... If we graph both equations there is exactly one point that will be true for both equations. This point is located at x,y or (-103.5, 88.8), and is the coordinate location of where they intersect.