Solve the following system of equations. 10x + 10y = 100 and 50x + 50y = 400

To begin, you'd want to put the 10x + 10y = 100 into y-intercept form. To do that, you'd subtract 10x from that side of the equation and add it to the side with the 100. So, now your equation would be 10y = -10x + 100. You want to get y by itself, so you'd divide the WHOLE equation by 10. Now you have    y= -x + 10.
Plug that into the second equation as y.
50x + 50(-x + 10) = 400
50x - 50x + 500 = 400
the two x's would cancel each other out, so in the end you get 500 = 400.
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