Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Entry Level Assessment - Multiple Choice - Page XXXIV: 1

Answer

We have x + y = -6 .... (1) x - y = 6 ..... (2) Adding equations (1) and (2), we get 2x = 0 x = 0 Substituting x = 0 in equation 1, we get x + y = -6 0 + y = -6 y = -6 So, x = 0 and y = -6 Hence, the point (0, -6) is the solution of two equations. That means, the 2 lines representing these 2 equations intersect each other in point (0, -6). This is shown in the graph. (The red line is x + y = -6 and blue line is x - y = 6) So to find common solution of 2 equations, solve those 2 equations by adding or subtracting and find values of x and y and then these values of x and y form a solution to the simultaneous equations.
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Work Step by Step

We have x + y = -6 x - y = 6 If we add these two together we get 2x = 0 x = 0 Substituting the value 0 for x into either of the original expressions gives: y = -6 so the point (0, -6) is the only one at which the two lines intersect. What we have are two lines, one with slope 1 and the other with slope -1, but both of which have the y-intercept -6. In general, Caitlin, if you find yourself having trouble with these sorts of problems, one of the easiest things you can do is the graph the equations on the same pair of coordinate axes.
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