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Question 657718: The sum of two numbers is 75. The second number is 3 less than twice the first. Find the two numbers.
Answer by colliefan(242)   (Show Source):
You can put this solution on YOUR website! If the two numbers are x and y, then the problem can be rewritten as these equations. Take y to be "the second number".
x+y=75
y=2x-3
The substitution method requires you to solve for one variable in one equation and then substitute the expression from one into the other. In this case, the second equation already has the y isolated so we can substitute from that one to the first.
x + (2x-3) =75
Now you have an equation with one variable and can solve for x.
x + (2x-3) =75
x + 2x-3 =75
3x-3 =75
3x - 3 + 3 =75 + 3
3x +0 =78
3x = 78
3x * 1/3 = 78 * 1/3
x * 1 = 26
x = 26
Substitute this value of x into either of the original equations and solve for y.
x+y=75
26+y=75
26+y-26=75-26
y+0=49
y=49
Substitute both values for x and y into the original equations to make sure that they are the solution.
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