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Question 53839This question is from textbook Algebra 2
: Graph the linear system and estimate the solution. Then check
the solution algebraically.
20. 2x + y = 13
5x - 2y = 1
This question is from textbook Algebra 2
Answer by rchill(405)   (Show Source):
You can put this solution on YOUR website! Solve both equations for y first. The first equation becomes  and the 2nd one becomes  . Because two points determine a line, you need to determine 2 ordered pairs per graph by using some values of x to determine y. You then plot those points per line, connect the points, and you'll have two lines. Those lines either intersect, are parallel, or are the same line. If they intersect, the solution is the point of intersection; if parallel, there is no solution; if the same, infinite solution. You estimate the solution by looking at the graph (see graph below). It appears the lines intersect at (3,7). To prove that algebraicly, subsitute their values into the original equations: 2*3+7=13, which simplifies to 6+7=13, which is 13=13. That's a true statement, so the ordered pair (3,7) works so far. On to the next equation: 5*3 - 2*7 = 1, which simplifies to 15-14=1, or 1=1. Once again, a true statement, so our solution is correct!
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