Grade 9Algebra
x-3y=4, 4x-3y=2 solve according to linear equation in two variables
x-3y=4, 4x-3y=2 solve according to linear equation in two variables
1 Answer
Askiitians Tutor Team
Approved Tutor Answer1 Day agoTo solve the system of linear equations given by x - 3y = 4 and 4x - 3y = 2, we can use the substitution or elimination method. Here, we'll use the elimination method for clarity.
Step 1: Align the Equations
We have the following equations:
- Equation 1: x - 3y = 4
- Equation 2: 4x - 3y = 2
Step 2: Eliminate One Variable
To eliminate y, we can subtract Equation 1 from Equation 2:
(4x - 3y) - (x - 3y) = 2 - 4
This simplifies to:
3x = -2
Step 3: Solve for x
Now, divide both sides by 3:
x = -2/3
Step 4: Substitute x Back to Find y
Next, substitute x = -2/3 into Equation 1:
-2/3 - 3y = 4
To isolate y, first add 2/3 to both sides:
-3y = 4 + 2/3
Convert 4 to a fraction: 4 = 12/3, so:
-3y = 12/3 + 2/3 = 14/3
Now, divide by -3:
y = -14/9
Final Solution
The solution to the system of equations is:
- x = -2/3
- y = -14/9
These values satisfy both original equations. Thus, the solution is complete!
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