Simple linear simultaneous equations problem.

Question

Sorry if this is an easy question, but for seem reason I struggle using the elimination method for simultaneous equations, and finally decided to ask why my method doesn’t work.

(I can solve this problem with other methods such as substitution, I just want to know what is wrong with this method).

However, the y-value isn’t 10/17. Please could someone point out my mistake.

Answer 1

With the elimination method, I have: $$\left\{\begin{matrix} 12x+9y=-12 \\ -12x+8y=-22 \end{matrix}\right.$$

If I sum up the two equation, I obatin: $17y=-34$ and so $y=-2$. Now substitute in $4x+3y=-4$ and obtain: $4x-6=-4$ so $x=\frac{1}{2}$.

Your error is simply: when you have done the difference between the two equation, you have sum up $-12$ and $22$; you would have done $-12-22=-34$.

Answer 2

For easy computation, by subtraction ($(2)-(1)$)

$$2x-7y=15$$

and

$$2(7y+15)+3y=-4$$

or

$$y=-\frac{34}{17}.$$