How to solve
3x+2y=4
2x-3y=7
3 x + 2 y = 4 Multiply both sides by 2
6 x + 4 y = 8
2 x - 3 y = 7 Multiply both sides by 3
6 x - 9 y = 21
6 x + 4 y = 8
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6 x - 9 y = 21
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6 x - 6 x + 4 y - ( - 9 y ) = 8 - 21
4 y + 9 y = 13
13 y = - 13 Divide both sides by 13
y = - 13 / 13 = - 1
Replace this value in equation:
3 x + 2 y = 4
3 x + 2 * ( - 1 ) = 4
3 x - 2 = 4 Add 2 to both sides
3 x = 4 + 2 = 6 Divide both sides by 3
x = 6 / 3 = 2
x = 2 , y = - 1
To solve the system of equations 3x + 2y = 4 and 2x - 3y = 7, you can use either the substitution method or the elimination method.
Let's solve it using the substitution method:
1. Solve one of the equations for one variable (in terms of the other variable). Let's solve the first equation for x.
3x + 2y = 4
3x = 4 - 2y
x = (4 - 2y) / 3
2. Substitute the expression for x into the other equation.
2x - 3y = 7
2((4 - 2y) / 3) - 3y = 7
((8 - 4y) / 3) - 3y = 7
3. Simplify and solve for y.
(8 - 4y) - 9y = 21
8 - 4y - 9y = 21
-13y = 13
y = -1
4. Substitute the value of y back into either of the original equations to solve for x.
Using the first equation: 3x + 2(-1) = 4
3x - 2 = 4
3x = 6
x = 2
The solution to the system of equations is x = 2 and y = -1.
Therefore, the system is consistent and has a unique solution.