X-3y=1
4x+5y=4
Solve the system of equations.
multiply the first by 4
4x-12y = 4
4x + 5y = 4
subtract them:
-17u = 0
y = 0
back into the first:
x - 0 = 1
x = 1
x = (3 y + 1)
4(3y+1) + 5 y = 4
12 y + 4 + 5 y = 4
17 y = 0
y = 0
x = 3*0 + 1 = 1
(1,0)
To solve the system of equations, you can use the method of substitution or the method of elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation, X - 3y = 1, for X in terms of y:
X = 1 + 3y.
Step 2: Substitute the expression for X in the second equation.
Using the above expression for X, substitute it into the second equation 4x + 5y = 4:
4(1 + 3y) + 5y = 4.
Step 3: Simplify and solve for y.
Distribute 4 into the parentheses:
4 + 12y + 5y = 4.
Combine like terms:
17y + 4 = 4.
Subtract 4 from both sides:
17y = 0.
Divide both sides by 17:
y = 0.
Step 4: Substitute the value of y back into either equation to solve for x.
Substitute y = 0 into the first equation X - 3y = 1:
X - 3(0) = 1.
Simplify:
X - 0 = 1.
Therefore, X = 1.
Step 5: Write the solution.
The solution to the system of equations is X = 1 and y = 0.