To find the x-intercept of a linear equation, let = 0 and solve for the other variable.
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You can solve for x and y in terms of z, then let z take on the value of the parameter.
Subtracting the first equation from the second, you get
... x_2 +x_3 = 1
Subtracting that from the first equation gives you
... x_1 +2x_3 = 3
Let x_3 = t. Then your parametric equations are ...