Help is Here!! Below is a step-by-step instruction guide on how to go about solving a sample problem!
I will use these two equations as samples.
2x + 5y = 4
5x - 7y = -29
First, solve one of the equations (it doesn't matter which) for either x or y (either variable is fine). I chose to solve the first equation for x and got x = -5/2y + 2. Next, plug this value into the other equation for the variable you have solved for (in this case, I will plug in -5/2y + 2 for x). Your resulting equation is as so:
5(-5/2y + 2) - 7y = -29
As you can see, I have substituted the x for -5/2y + 2. I can do this because we figured out when isolating x that x = -5/2y + 2. Therefore, the value of the equation isn't changed when making this substitution in other equations. Moving on...
Our next step is to solve this equation,
5(-5/2y + 2) - 7y = -29, for y. It will take quite a few steps, but eventually y will be isolated to 2. You now have your value for y: y=2. Now all you have to do is substitute this value in for y in your other equation, 2x + 5y = 4. Your equation, once you have plugged in the y value, will appear as such:
2x + 5(2) = 6
Solve this equation for x. It will equal -3. Last, just plug in the x and y values to their spots on the coordinate. The final answer for his sample will be (-3,2).
PS - Remember, as I mentioned in the beginning of this answer, you did not have to follow is particular method. You could have substituted a different value, and you could have also begun with the other equation.
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What's weird is that I'm in 9th grade geometry. I took and aced algebra 1 last year, which is how I know so much about the subject.