SOLUTION: Solve by elimination: 1.8x + 11y= 20 5x - 11y= -59 2. 2x + 18y= -9 4x + 18y= -27 3. 20x + 3y= 20 -20x + 5y= 60 4. 3x - 10y= -25 4x + 40y= 20 5. 7x + 15y= 32 x

Algebra ->  Expressions-with-variables -> SOLUTION: Solve by elimination: 1.8x + 11y= 20 5x - 11y= -59 2. 2x + 18y= -9 4x + 18y= -27 3. 20x + 3y= 20 -20x + 5y= 60 4. 3x - 10y= -25 4x + 40y= 20 5. 7x + 15y= 32 x       Log On


   

Question 125597This question is from textbook
: Solve by elimination:
1.8x + 11y= 20
5x - 11y= -59
2. 2x + 18y= -9
4x + 18y= -27
3. 20x + 3y= 20
-20x + 5y= 60
4. 3x - 10y= -25
4x + 40y= 20
5. 7x + 15y= 32
x - 3y= 20
6. x - 8y= 18
-16 + 16y= -8
7. 24x + 2y= 52
6x - 3y= -36
8. 88x - 5y=39
-8 + 3y= -1
9. 2x + 4y= 8
5x + y= -7
10. 3x + 2y= -9
-10x + 5y= -26
11. 4x + 5y= 15
6x - 4y= 11
12. 3x - 2y= 10
2x + 3y= -2
13. -2x + 5y= 20
3x - 7y= -26
14. 10x + 8y= 2
8x + 6y= 1
15. 9x + 5y= 34
8x - 2y= -2
 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to help you get started

# 1





Start with the given system of equations:

system%288x%2B11y=20%2C5x-11y=-59%29



Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.





In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).


So lets eliminate x. In order to do that, we need to have both x coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.



So to make the x coefficients equal in magnitude but opposite in sign, we need to multiply both x coefficients by some number to get them to an common number. So if we wanted to get 8 and 5 to some equal number, we could try to get them to the LCM.



Since the LCM of 8 and 5 is 40, we need to multiply both sides of the top equation by 5 and multiply both sides of the bottom equation by -8 like this:




5%288x%2B11y%29=5%2820%29 Multiply the top equation (both sides) by 5
-8%285x-11y%29=-8%28-59%29 Multiply the bottom equation (both sides) by -8




Distribute and multiply

40x%2B55y=100
-40x%2B88y=472


Now add the equations together. In order to add 2 equations, group like terms and combine them

%2840x-40x%29%2B%2855y%2B88y%29=100%2B472

Combine like terms and simplify



cross%2840x-40x%29%2B143y=572 Notice how the x terms cancel out




143y=572 Simplify




y=572%2F143 Divide both sides by 143 to isolate y




y=4 Reduce



Now plug this answer into the top equation 8x%2B11y=20 to solve for x

8x%2B11y=20 Start with the first equation



8x%2B11%284%29=20 Plug in y=4



8x=20-44Subtract 44 from both sides


8x=-24 Combine like terms on the right side


x=%28-24%29%2F%288%29 Divide both sides by 8 to isolate x



x=-3 Divide




So our answer is
x=-3 and y=4



which also looks like




Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of 8x%2B11y=20 (red) and 5x-11y=-59 (green) and the intersection of the lines (blue circle).






# 2




Start with the given system of equations:

system%282x%2B18y=-9%2C4x%2B18y=-27%29



Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.





In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).


So lets eliminate x. In order to do that, we need to have both x coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.



So to make the x coefficients equal in magnitude but opposite in sign, we need to multiply both x coefficients by some number to get them to an common number. So if we wanted to get 2 and 4 to some equal number, we could try to get them to the LCM.



Since the LCM of 2 and 4 is 4, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this:




2%282x%2B18y%29=2%28-9%29 Multiply the top equation (both sides) by 2
-1%284x%2B18y%29=-1%28-27%29 Multiply the bottom equation (both sides) by -1




Distribute and multiply

4x%2B36y=-18
-4x-18y=27


Now add the equations together. In order to add 2 equations, group like terms and combine them

%284x-4x%29%2B%2836y-18y%29=-18%2B27

Combine like terms and simplify



cross%284x-4x%29%2B18y=9 Notice how the x terms cancel out




18y=9 Simplify




y=9%2F18 Divide both sides by 18 to isolate y




y=1%2F2 Reduce



Now plug this answer into the top equation 2x%2B18y=-9 to solve for x

2x%2B18y=-9 Start with the first equation



2x%2B18%281%2F2%29=-9 Plug in y=1%2F2



%282%29%282x%2B18%2F2%29=%282%29%28-9%29 Multiply both sides by the LCM of 2. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



4x%2B18=-18 Distribute and multiply the LCM to each side



4x=-18-18Subtract 18 from both sides


4x=-36 Combine like terms on the right side


x=%28-36%29%2F%284%29 Divide both sides by 4 to isolate x



x=-9 Divide




So our answer is
x=-9 and y=1%2F2



which also looks like




Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of 2x%2B18y=-9 (red) and 4x%2B18y=-27 (green) and the intersection of the lines (blue circle).