Solve this system by elimination. SHOW ALL OF YOUR WORK.
5x-4y=3
-10x+7y=-4​

Hi! Your answer is x = -1, y = -2. We can write in coordinate form as (-1,-2)

Please see an explanation for a better and clear understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Step-by-step explanation:

By elimination method, we can eliminate either x-term or y-term. It depends on your choice or desire. Notice that both equations cannot be eliminated because if we add x-term up, we would get -5x which doesn't even eliminate x-term. Same goes to y-term. Now the question will pop up in your head - Then how do we eliminate either x-term or y-term?

Simple, multiply the whole equation to make one of the terms have same absolute value. Notice if we multiply the whole first equation by 2, we would get x-term from 5x to 10x. Then we add 10x and -10x up, we would get 0 and finally get x-term to be eliminated.

Therefore, multiply the whole first equation by 2.

Next, rewrite the equation.

Then we are able to eliminate x-term by adding up between first and second equation.

We've finally got the y-value. But we are not done yet. What we are going to do next is to find x-value.

Simply substituting y = -2 in any given equations. You can either substitute y = -2 in one equation only if you are pretty certain enough or two equations if you think that you value safety/quality more than time. I'll be substituting y = -2 in two equations to demonstrate how substituting the solution in two equations get you to the same answer.

Substituting in First Equation

Substitute y = -2 in the equation. It's the best to use an original equation instead of rewritten equation.

Substituting in Second Equation

Substitute y = -2 in the equation.

Notice how substituting in two equations give the exact same answer in the end. We've finally got the solution.

We can conclude that when x = -1, y =-2.