Use algebraic method to solve line 1 x+4y=14 line a 3x+2y=12
algebraic method?
x+4y=14
3x+2y=12
multipy the first equation by 3
3x+12y=42
3x+2y=12
subtract the second equation from the first.
10y=30
y=3
put that value of y into either equation, and solve for x.
x=2
To solve the system of equations using the algebraic method, we can use either the substitution method or the elimination method. Let's use the elimination method to solve the system.
Given the equations:
Line 1: x + 4y = 14 ...(1)
Line 2: 3x + 2y = 12 ...(2)
To eliminate one variable, we'll multiply equation (1) by 3 and equation (2) by 1:
3(x + 4y) = 3(14)
3x + 12y = 42 ...(3)
1(3x + 2y) = 1(12)
3x + 2y = 12 ...(4)
Now we'll subtract equation (4) from equation (3) to eliminate the x variable:
(3x + 12y) - (3x + 2y) = 42 - 12
3x - 3x + 12y - 2y = 30
This simplifies to:
10y = 30
Next, divide both sides of the equation by 10 to solve for y:
10y/10 = 30/10
y = 3
After finding the value of y, we substitute it back into either equation (1) or (2) to solve for x. Let's use equation (1):
x + 4(3) = 14
x + 12 = 14
Subtract 12 from both sides:
x = 14 - 12
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 3.