Question 51650: What is the answer to x=4 and 2x-3y=-19
Answer by rchill(405)   (Show Source):
You can put this solution on YOUR website! The solution to two linear equations will either be a point (where they intersect), all points (the lines are the same), or no solution (the lines are parallel). The first equation is a vertical line at x=4. Solving for y in the second equation, first add 3y to both sides to get  . Next, add 19 to both sides to get  . Dividing both sides by 3 yields  . So now we graph each equation to see where they intersect:  . It appears to the eye they intersect at (4,8.5). But we don't have to rely on our eyes here or the ability to read a graph with coordinates. Because the first equation is x=4, that vertical line will cross our other line no matter what (unless they're parallel or the same line). You can calculate where they intersect by substituting 4 for x in . We get  which simplifies to  , which further reduces to  , or  . Therefore, the solution is (4,9).
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