Solve each system by elimination.
a. 2x + 3y = 33
y= 1/4x
elimination would be a poor choice for this one , why not use substitution ?
y = (1/4)x into the first .....
2x + 3(1/4)x = 33
times 4
8x + 3x = 132
11x = 132
x = 12
then y = (1/4)(12) = 3
x=12 , y = 3
by elimination:
work on the 2nd
4y = x
x - 4y = 0
times 2
2x - 8y = 0
so now:
2x + 3y = 33
2x - 8y = 0
subtract them:
11y = 33
y = 3
sub into x - 4y = 0
x - 12 = 0
x = 12
so x = 12, y = 3
same as above.
To solve this system by elimination, we need to eliminate either x or y by manipulating the equations.
The second equation is already in the form y = mx + b, which means we can easily eliminate y by multiplying the equations.
First, we will multiply the second equation by 4 to eliminate the fraction:
4(y) = 4(1/4x)
4y = x
Now, we have the system:
2x + 3y = 33
4y = x
To eliminate y, we can substitute 4y for x in the first equation:
2(4y) + 3y = 33
8y + 3y = 33
11y = 33
y = 33/11
y = 3
Now, substitute y = 3 back into the second equation to find x:
4(3) = x
12 = x
So, the solution to the system of equations is x = 12 and y = 3.
To solve the system of equations using elimination, we want to eliminate one of the variables by adding or subtracting the equations.
Let's start by simplifying the second equation. We can rewrite it as y = 1/4x as given.
Now, we can use elimination to eliminate y. To do this, we need to get the coefficients of y in both equations to be the same (or multiples of each other). In this case, we can multiply the second equation by 12 to make the coefficient of y the same as the first equation.
Multiplying the second equation by 12, we get:
12y = 3x
Now we can rewrite the system of equations:
First equation: 2x + 3y = 33
Second equation: 12y = 3x
Now let's eliminate y. We can do this by multiplying the second equation by -1/3 and adding it to the first equation:
-1/3 * (12y) = -1/3 * (3x)
Simplifying, we get:
-4y = -x
Now let's add the equations together:
2x + 3y + (-4y) = 33 + (-x)
Simplifying, we get:
2x - x = 33
Combining like terms, we have:
x = 33
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the second equation:
y = 1/4 * x
y = 1/4 * 33
y = 33/4
So the solution to the system of equations is:
x = 33
y = 33/4