solve by elimination method 5x+2y=-13, 7x-3y=17
The cleanest way to do this would be to multiply one by 3 and 2 all the way, respectively. 15x+6y=39 and 14x-6y=34. With the y's dropping out because 6 and -6 are opposite pairs adding to zero, adding gets one 29x=73. Divide each side by 29 to get what x is, and then use whatever you get for x to go back and find y. Do you now see why this is called the elimination method?
To solve the system of equations using the elimination method, you need to eliminate one variable by adding or subtracting the two equations. Here's how you can solve the given system of equations:
1. Rearrange both equations so that the variables line up vertically:
5x + 2y = -13
7x - 3y = 17
2. Multiply both sides of one equation by a constant so that the coefficients of one of the variables will have the same absolute value, but opposite signs when added together.
Let's multiply the second equation by 2 to make the coefficients of y the same but opposite:
5x + 2y = -13
14x - 6y = 34
3. Now, you can add the two equations together. By doing this, the y variable will be eliminated because 2y and -6y add up to zero.
(5x + 2y) + (14x - 6y) = (-13) + 34
5x + 14x + 2y - 6y = 21
19x - 4y = 21
4. Simplify the resulting equation:
19x - 4y = 21
5. Now, solve this new equation for one variable in terms of the other variable. Let's solve for x:
19x = 4y + 21
x = (4y + 21) / 19
6. Substitute this value of x back into one of the original equations to solve for y. Let's use the first equation:
5x + 2y = -13
5((4y + 21) / 19) + 2y = -13
Simplify this equation to solve for y.
By following these steps, you will find the values of x and y that satisfy both equations.