Solve the following systems of equations.
3x + 4y = 4
2x + y = 6
2 x + y = 6 Subtract 2 x to both sides
2 x + y - 2 x = 6 - 2x
y = 6 - 2x
3 x + 4 y = 4
3 x + 4 ( 6 - 2 x ) = 4
3 x + 24 - 8 x = 4
- 5 x + 24 = 4 Subtract 24 to both sides
- 5 x + 24 - 24 = 4 - 24
- 5 x = - 20 Divide both sides by - 5
- 5 x / - 5 = - 20 / - 5
x = 4
y = 6 - 2x
y = 6 - 2 * 4
y = 6 - 8 = - 2
Solution :
x = 4 , y = - 2
To solve the system of equations, we will use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y in terms of x.
2x + y = 6
y = 6 - 2x
Step 2: Substitute the expression for y into the other equation.
Now, substitute the expression for y into the first equation.
3x + 4(6 - 2x) = 4
Step 3: Simplify and solve for x.
Distribute the 4 into (6 - 2x):
3x + 24 - 8x = 4
Combine like terms:
-5x + 24 = 4
Subtract 24 from both sides:
-5x = 4 - 24
-5x = -20
Divide by -5:
x = -20 รท -5
x = 4
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Let's use the second equation to find y:
2(4) + y = 6
8 + y = 6
Subtract 8 from both sides:
y = 6 - 8
y = -2
Therefore, the solution to the system of equations is x = 4 and y = -2.