SOLUTION: To solve systems of equations by the substitution method. My son needs help with these 2 problems: (1) x = 3y – 1 x +2y = 9 (2) 2x – 3y = 12 x = 4y +1

Algebra ->  Equations -> SOLUTION: To solve systems of equations by the substitution method. My son needs help with these 2 problems: (1) x = 3y – 1 x +2y = 9 (2) 2x – 3y = 12 x = 4y +1       Log On


   

Question 64463: To solve systems of equations by the substitution method. My son needs help with these 2 problems:
(1) x = 3y – 1
x +2y = 9
(2) 2x – 3y = 12
x = 4y +1

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1) x = 3y – 1
x +2y = 9
Substitue the value of x in the 1st equation into the 2nd equation to get:
(3y-1)+2y=9
5y-1=9
5y=10
y=2
Substitute that value into the 1st equation to solve for x as follows:
x=3(2)-1
x=5
Sustitute x=5 and y=2 into the 2nd equation to check the solution.
5+2(2)=9
5+4=9
9=9
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SOLUTIOn: x=5 y=2
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(2) 2x – 3y = 12
x = 4y +1
Substitute the value for x in the 2nd equation into the 1st equation:
2(4y+1)-3y=12
8y+2-3y=12
5y=10
y=2
Substitute into the 2nd equation to solve for x, as follows:
x=4(2)+1
x=9
Check in the 1st equation:
2(9)-3(2)=12
18-6=12
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SOLUTION: x=9, y=2
Cheers,
Stan H.


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by substitution:
1) x+=+3y-1 Substitute this equation for x into the second equation and solve for y.
x%2B2y+=+9
%283y-1%29%2B2y+=+9 Simplify and solve for y.
3y%2B2y-1+=+9 Add the y-terms.
5y-1+=+9 Add 1 to both sides of the equation.
5y+=+10 Finally, divide both sides by 5.
y+=+2 Now substitute this value of y into the first equation and solve for x.
x+=+3%282%29-1
x+=+6-1
x+=+5
The solution is: (5, 2)
2) 2x-3y+=+12
x+=+4y%2B1 Substitute this equation for x into the first equation and solve for y.
2%284y%2B1%29-3y+=+12 Simplify and solve for y.
8y%2B2-3y+=+12 Combine the y-terms.
5y%2B2+=+12 Subtract 2 from both sides of the equation.
5y+=+10 Finally, divide both sides by 5.
y+=+2 Now substitute this value for y into the second equation and solve for x.
x+=+4%282%29%2B1
x+=+8%2B1
x+=+9
The solution is: (9, 2)