3x-2y=4
2x-3y=6. using substitution method
Multiply Eq1 by 2 and Eq2 by 3. Subtract Eq2 from Eq1:
6x-4y = 8.
6x-9y = 18.
Diff.:5y = -10
Y = -2.
3x-2y = 4.
3x-2*(-2) = 4.
X =
3x + 2y = -5
To solve the given system of equations using the substitution method, follow these steps:
1. Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for x:
3x - 2y = 4
3x = 2y + 4
x = (2y + 4) / 3
2. Substitute the expression found for x in the other equation.
Replace x in the second equation with (2y + 4) / 3:
2((2y + 4) / 3) - 3y = 6
(4y + 8) / 3 - 3y = 6
Multiply both sides of the equation by 3 to eliminate the fraction:
4y + 8 - 9y = 18
3. Simplify and solve for y.
Combine like terms: -5y + 8 = 18
Subtract 8 from both sides: -5y = 10
Divide by -5: y = -2
4. Substitute the value of y into one of the original equations to solve for x.
Let's use the first equation:
3x - 2(-2) = 4
3x + 4 = 4
Subtract 4 from both sides: 3x = 0
Divide by 3: x = 0
Therefore, the solution to the system of equations is x = 0 and y = -2.
2x = 3y+6, so
3x = 3/2 (3y+6)
now use that to get
3/2 (3y+6) - 2y = 4
solve for y, and then you can get x.