solve the linear system by using elimination.
x-1/2y = 11/2
-x+4y = 26
i cant ever seem to get an answer that isn't nonterminating.
Just add the two together as they are then divde the term with no variable by the one with a variable to get your answer.
To solve the linear system using elimination, we'll eliminate one variable by adding or subtracting the two equations. Let's start by multiplying the first equation by 2 to eliminate the fraction:
2(x - 1/2y) = 2(11/2)
2x - y = 11
Now we have the following system:
2x - y = 11 (Equation 1)
-x + 4y = 26 (Equation 2)
To eliminate the variable x, we can add the two equations:
(2x - y) + (-x + 4y) = 11 + 26
Simplifying the equation, we get:
2x - x - y + 4y = 37
x + 3y = 37 (Equation 3)
Now we have two equations:
x + 3y = 37 (Equation 3)
-x + 4y = 26 (Equation 2)
To eliminate the variable x, we can add the two equations:
(x + 3y) + (-x + 4y) = 37 + 26
Simplifying the equation, we get:
x - x + 3y + 4y = 63
7y = 63
To solve for y, we divide both sides of the equation by 7:
7y/7 = 63/7
y = 9
Now that we have the value of y, we can substitute it into Equation 3 to find x:
x + 3(9) = 37
x + 27 = 37
To isolate x, we subtract 27 from both sides:
x + 27 - 27 = 37 - 27
x = 10
Therefore, the solution to the linear system is x = 10 and y = 9.
To solve a linear system using elimination, follow these steps:
Step 1: Multiply one or both equations by a constant to make the coefficients of either x or y in one equation equal to the coefficients in the other equation but with opposite signs. This will allow the terms to cancel out when added together.
Step 2: Add the equations together so that one variable is eliminated. This will result in a new equation with only one variable.
Step 3: Solve the new equation for the remaining variable.
Step 4: Substitute the value found in step 3 back into one of the original equations to solve for the other variable.
Let's apply these steps to your system of equations:
Equation 1: x - 1/2y = 11/2
Equation 2: -x + 4y = 26
We'll start by eliminating the x-term. To do this, we'll multiply Equation 2 by 1 to make the coefficient of x opposite in sign to the coefficient in Equation 1. We now have:
Equation 1: x - 1/2y = 11/2
Equation 2: -x + 4y = 26
Now, add the equations together:
(x - 1/2y) + (-x + 4y) = (11/2) + 26
x - 1/2y - x + 4y = 23/2 + 26
(4y - 1/2y) = 23/2 + 26
(8y - y) = 23/2 + 26
7y = 23/2 + 26
Next, simplify and solve for y:
7y = 23/2 + 26
7y = 23/2 + 52/2
7y = 75/2
y = 75/2 ÷ 7
y = 75/2 × 1/7
y = 75/14
y ≈ 5.357
Now that we have the value of y, we can substitute it back into one of the original equations (Equation 1, for example) to solve for x:
x - 1/2(5.357) = 11/2
x - 2.679 = 5.5
x = 5.5 + 2.679
x ≈ 8.179
So the solution to the linear system is x ≈ 8.179 and y ≈ 5.357.