3x+y=6
4x+2y=8
how do you solve this?
3x+y=6
4x+2y=8
substitute
y = -3x + 6
4x+ 2(-3x + 6) = 8
4x -6x +12 = 8
-2x + 12 = 8
-2x = -4
x = 2
y = -3x + 6
y = -3(2) + 6
y = 0
(2,0)
3x+y=6
4x+2y=8
y = 6 - 3x
4x + 2(6 - 3x) = 8
4x + 12 -6x = -4
-2x = -8
x = 2
Substitute 2 for x in the first equation to find the value of y.
To solve this system of equations:
Step 1: Choose one of the equations and solve for one variable in terms of the other. Let's choose the first equation, 3x + y = 6.
- Subtract 3x from both sides: y = -3x + 6.
Step 2: Substitute this expression for y in the second equation. Replace y in the equation 4x + 2y = 8 with -3x + 6.
- The equation becomes: 4x + 2(-3x + 6) = 8.
- Simplify and solve for x: 4x - 6x + 12 = 8.
- Combine like terms: -2x + 12 = 8.
- Subtract 12 from both sides: -2x = -4.
- Divide by -2: x = 2.
Step 3: Substitute the value of x back into one of the original equations to solve for y. Using the first equation, 3x + y = 6:
- Substitute x = 2: 3(2) + y = 6.
- Simplify: 6 + y = 6.
- Subtract 6 from both sides: y = 0.
The solution to the system of equations is x = 2 and y = 0.