Using substitution, solve this equation..
3x - 5y = 11
x - 3y = 1
Equation 2 looks like it would be easy to solve for x, so we take it and isolate x:
x - 3y = 1
x = 1 + 3 y
Now we can use this result and substitute x = 1 + 3 y in for x in equation 1:
3x - 5y = 11
3 * ( 1 + 3 y ) - 5 y = 11
3 + 9 y - 5 y = 11
3 + 4 y = 11
4 y = 11 - 3
4 y = 8 Divide both sides with 4
y = 2
x = 1 + 3 y
x = 1 + 3 * 2
x = 1 + 6
x = 7
To solve this system of equations using substitution, we can express one variable in terms of the other in one equation and substitute it into the other equation.
Let's solve for x in terms of y in the second equation:
x - 3y = 1
x = 1 + 3y
Now we substitute this expression for x in the first equation:
3x - 5y = 11
3(1 + 3y) - 5y = 11
3 + 9y - 5y = 11
4y = 8
y = 2
Now that we have found the value of y, we can substitute it back into either of the original equations to find the value of x.
Let's substitute y = 2 into the second equation:
x - 3(2) = 1
x - 6 = 1
x = 7
Therefore, the solution to the system of equations is x = 7 and y = 2.
To solve this system of equations using substitution, we'll solve one of the equations for one variable and substitute it into the other equation.
Let's solve the second equation for x:
x - 3y = 1
First, let's isolate x by adding 3y to both sides:
x = 1 + 3y
Now, substitute this expression for x in the first equation:
3x - 5y = 11
3(1 + 3y) - 5y = 11
Distribute the 3 to both terms inside the parentheses:
3 + 9y - 5y = 11
Combine like terms:
3 + 4y = 11
Subtract 3 from both sides:
4y = 8
Divide both sides by 4:
y = 2
Now, substitute this value of y back into the second equation to find x:
x - 3y = 1
x - 3(2) = 1
x - 6 = 1
Add 6 to both sides:
x = 7
So, the solution to the system of equations is x = 7 and y = 2.