How do you solve the system #y=1/2x+4# and #y=-4x-5# by graphing?

1 Answer
Mar 17, 2016

Answer:

The equations are in standard form, #y=mx+c#, where #m# is the slope (gradient) and #c# is the y-intercept. Using this, graph as shown below to find the solution #(-2,3)#.

Explanation:

The solution of this set of simultaneous linear equations is the point where the lines cross.

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You can read from the graph that this point is #(-2,3)#.

The equations can also be solved algebraically (as a way of checking your answer) by equating the two equations with one another:

#1/2x+4=-4x-5#

Double to make it neater:

#x+8 = -8x-10#

Add #8x# both sides and subtract 8 from both sides:

#9x=-18# which gives #x=-2#

Substitute back into either equation to find #y=3#.