I can figure out how to use elimination here. I tried but I didn't do it right.
13x + 10y = 203 26x + 18y = 394
How do you use elimination to find the point of intersection?
13x + 10y = 203
26x + 18y = 394
multiply the 1st equation by 2 and subtract the 2nd, and you have
2y = 12
and the x has been eliminated.
Wait so you're suposed to subtract the problem?
I was taught to add them.... THAT'S WHY I NEVER GOT IT RIGHT!
well, I guess you could multiply by -2 and then add. Same "difference" in the "sun" total, yeah?
To use the elimination method to find the point of intersection between the two equations, you need to eliminate one variable by effectively adding or subtracting the two equations. Here's how you can do it step by step:
1. Multiply one or both of the equations by suitable numbers in order to make the coefficients of either x or y in both equations opposites of each other (e.g., if one equation has a coefficient of 13x and the other equation has a coefficient of 26x, you can multiply the first equation by 2 to make it 26x, and then the coefficients of x will be opposites).
2. Once you have made one set of coefficients opposites, you can add the two equations together (or subtract them, depending on the scenario). This will result in one equation with a single variable, allowing you to solve for it.
Let's apply these steps to your example:
Given equations:
13x + 10y = 203
26x + 18y = 394
To eliminate the x variable, we can multiply the first equation by 2:
2(13x + 10y) = 2(203)
26x + 20y = 406
Now we can subtract the second equation from the modified first equation:
(26x + 20y) - (26x + 18y) = 406 - 394
2y = 12
Simplifying further, we have:
2y = 12
To solve for y, divide both sides of the equation by 2:
y = 12/2
y = 6
Now that you have the value of y, you can substitute it back into either of the original equations and solve for x. Let's use the first equation:
13x + 10(6) = 203
13x + 60 = 203
Subtract 60 from both sides of the equation:
13x = 143
Divide both sides of the equation by 13:
x = 11
Therefore, the point of intersection of the two equations is (x, y) = (11, 6).
Remember, when using the elimination method, it's essential to choose the right equations and manipulate them correctly to eliminate one variable at a time.