232k views
4 votes
Solve the system using addition. Use pencil and paper. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x​ first, is the addition method still a good​ choice? Explain.

x-2.5y=12.5
-x+2.3y=11.9

1 Answer

5 votes

Answer: the answers are x = -292.5 and y = -122

Explanation:

Elimination is combining equations to obtain an equation with just one variable. This is only possible if the coefficients of one variable in both equations are opposed and will cancel each other out when put together. Elimination is most effective when it occurs naturally in the equations, but equations may also be modified to produce typical coefficients by multiplying or dividing equations by a given value. The next step would be to utilize the equation we devised to determine the variable's worth and then insert that value back into the original equation to determine the remaining variable.

For solving the question to find x we have to make the coefficients of y the same. for that, we will multiply the first equation by 2.3 and the second equation by 2.5.

After that, we get the 2 equations as

2.3x-5.75y = 28.75

-2.5x+5.75y = 29.75

then by adding the 2 equations we get

-0.2x = 58.5

and by dividing 58.5 by -0.2 we get

x = -292.5

substituting the value of x in any equations above we get

y = -122

User BlackHoleDetector
by
4.4k points