Solve by substitution :addition, substration or multiplication
4X+3Y=19 and 6X+3Y=33
X= Y=
This time, subtract the first equation from the second.
To solve the system of equations by substitution, we will start by solving one of the equations for one variable in terms of the other variable. Then, we will substitute this expression into the other equation and solve for the remaining variable.
Let's solve the first equation, 4X + 3Y = 19, for X in terms of Y.
Step 1: Subtract 3Y from both sides of the equation:
4X = 19 - 3Y
Step 2: Divide both sides of the equation by 4 to isolate X:
X = (19 - 3Y) / 4
Now, we will substitute this expression for X into the second equation, 6X + 3Y = 33.
Step 3: Replace X with (19 - 3Y) / 4 in the second equation:
6((19 - 3Y) / 4) + 3Y = 33
Step 4: Simplify the equation:
Multiply 6 by each term in the parentheses:
(6*19 - 6*3Y) / 4 + 3Y = 33
Let's simplify further:
(114 - 18Y)/4 + 3Y = 33
Step 5: Multiply all terms in the equation by 4 to eliminate the fraction:
114 - 18Y + 12Y = 132
Combine like terms:
114 - 6Y = 132
Step 6: Subtract 114 from both sides of the equation:
-6Y = 132 - 114
Simplify:
-6Y = 18
Step 7: Divide both sides of the equation by -6 to solve for Y:
Y = 18 / -6
Simplify:
Y = -3
Now that we have the value of Y, we can substitute it back into one of the original equations to solve for X:
Using the first equation, 4X + 3Y = 19:
4X + 3(-3) = 19
Simplify:
4X - 9 = 19
Step 8: Add 9 to both sides of the equation:
4X = 28
Step 9: Divide both sides of the equation by 4 to solve for X:
X = 28 / 4
Simplify:
X = 7
Therefore, the solution to the system of equations 4X + 3Y = 19 and 6X + 3Y = 33 is X = 7 and Y = -3.