Question 950578: Use substitution to solve the following linear system.
X+1/2y=7
3x+2y=18
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! The idea here is to solve one of the equations for one of the variables, and plug this into the other equation. It does not matter which equation or which variable you pick. The result will be the same. I'll solve for x in the first equation because it's the easiest:
x+1/2y = 7
x = 7-1/2y Now we have a value for x, let's proceed:
3(7-1/2y)+ 2y = 18
21 - 1 1/2y + 2y = 18 Add the y on the left and subtract 21 on both sides
1/2y = -3 now divide both sides by 1/2, remember to divide by a fraction you flip the dividing fraction and multiply. -3 becomes -3/1.
y = -3/1* 2/1
y= -6 Now take your first equation:
x + 1/2(-6)= 7
x + -3 = 7
x = 10 Now solve the second equation, with the values we got for x and y:
3(10)+2(-6)=18 Do the operations:
30 - 12 = 18 How do you like it, we got the right answer! ;-)
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