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Question 46286: ok so without doing any graphing, we need to determine whether the system has 1, no, or infinite solutions.
x + 2y = 6
y = - 1/2x + 3
thanks a bunch
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! You can solve this in a couple of ways:
1) Rewrite the first equation in the slope-intercept form.
x+2y = 6 Subtract x from both sides.
2y = -x+6 Now divide both sides by 2.
y = -1/2x + 3 Compare this with second equation:
y = -1/2x + 3 ...they are identical meaning that they are the same line, so the number of solutions is infinite.
2) Solve by substitution. Substitute the second equation (y = -1/2x + 3) into the first equation and solve for x.
x + 2(-1/2x+3) = 6
x + (-x+6) = 6
6 = 6 Since the variable x has dropped out, it means that any value of x will satisfy the equations, hence, the number of solutions is infinite.
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