Question 232463
Solve the system of equations:
{{{x+y = 13}}}
{{{x-y = -3}}} We can eliminate the y-variable by adding these two equations.
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{{{2x = 10}}} Now divide both sides by 2.
{{{highlight(x = 5)}}} Substitute this value of x into either one of the two given equations to find the value of y.
{{{x+y = 13}}} Substitute x = 5.
{{{5+y = 13}}} Subtract 5 from both sides.
{{{highlight(y = 8)}}}
The solution is: (5, 8) and the system "consistent" since it has at least one solution.
You could also have solved this by graphing the two given equations. The "solution" is the point of intersection of the two lines (5, 8).
Let's look at the graph:
{{{graph(400,400,-5,15,-5,15,-x+13,x+3)}}}