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How To Solve Simple Bilinear Equations Under Extra Linear Constraints?

Solve each system of equations by graphing. If the system is inconsistent or the equations are dependent, say?

  • Answer:

    The easiest way to graph equations like this is to find their x- and y- intercepts. That will give you two points, and since these are linear equations, all you need is a straight line through the two points to graph each one. To find the x-intercept of each equation, set y to zero and solve for x. To find the y-intercept of each equation, set x to zero and solve for y. 2x - y = 4 has x-intercept (2,0) and y-intercept (0,-4). 4x + y = 2 has x-intercept (1/2,0) and y-intercept (0,2). Graph these and you'll see the lines intersect at (1,-2). If you substitute that point's coordinates, x=1 and y= -2, in the equations, you'll see it satisfies both of them. It's the only point that's on both lines, so its coordinates represent the common solution to both equations.

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The easiest way to graph equations like this is to find their x- and y- intercepts. That will give you two points, and since these are linear equations, all you need is a straight line through the two points to graph each one. To find the x-intercept of each equation, set y to zero and solve for x. To find the y-intercept of each equation, set x to zero and solve for y. 2x - y = 4 has x-intercept (2,0) and y-intercept (0,-4). 4x + y = 2 has x-intercept (1/2,0) and y-intercept (0,2). Graph these and you'll see the lines intersect at (1,-2). If you substitute that point's coordinates, x=1 and y= -2, in the equations, you'll see it satisfies both of them. It's the only point that's on both lines, so its coordinates represent the common solution to both equations.

Samwise

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