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Algebra Help By 4 Today Please
7 Answers
Without graphing, determine if the following system will have one solution, no solution, or an infinite number of solutions.
2x - y = 3
y = x + 4
2x - y = 3
y = x + 4
Answers
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For more on marking an answer as the "Best Answer", please visit our FAQ.Rearrange the equations so they look the same:
2x-y = 3
x - y = -4
Now subtract the bottom one from the top one - this will make the ys disappera and leave:
x = 7 (3--4)
Substitute x + 7 into the firat to get
14 - y = 3
So y = 11
Check that works in the other equation
11 = 7 +4
So there is only 1 solution, x=7, y = 11
2x-y = 3
x - y = -4
Now subtract the bottom one from the top one - this will make the ys disappera and leave:
x = 7 (3--4)
Substitute x + 7 into the firat to get
14 - y = 3
So y = 11
Check that works in the other equation
11 = 7 +4
So there is only 1 solution, x=7, y = 11
You don't even need to solve the simultaneous equations here.
You could simply rearrange these into:
y= 2x-3 and y= x+4
These are two straight lines with different gradients (2 and 1 respectively), so they can't be parallel. They must therefore meet and can only do so at one point. So there can only be one solution
You could simply rearrange these into:
y= 2x-3 and y= x+4
These are two straight lines with different gradients (2 and 1 respectively), so they can't be parallel. They must therefore meet and can only do so at one point. So there can only be one solution