Elimination

4x-7y=23
3y=-6x+33

To solve this system of equations, you can use the elimination method. The goal is to eliminate one of the variables by adding or subtracting the two equations.

First, let's multiply the second equation by 4 to make the coefficients of x match:

4(3y) = 4(-6x + 33)
12y = -24x + 132

Now, we can write the system of equations as:

4x - 7y = 23
-24x + 12y = 132

Next, we will eliminate the x variable by adding the equations together.

(4x - 7y) + (-24x + 12y) = 23 + 132

Combining like terms:

-20x + 5y = 155

Now we have one equation with just y.

To continue solving for y, we need to isolate y.

Let's multiply each term by 1/5 to simplify the equation:

(1/5)(-20x + 5y) = (1/5)(155)

Simplifying further:

-4x + y = 31

Now, we have the equation -4x + y = 31.

To solve for x, we can substitute this equation into the original first equation:

4x - 7y = 23

Substituting y with -4x + 31:

4x - 7(-4x + 31) = 23

Expanding:

4x + 28x - 217 = 23

Combining like terms:

32x - 217 = 23

To isolate x, we will add 217 to both sides:

32x - 217 + 217 = 23 + 217

Simplifying:

32x = 240

Now, divide both sides by 32 to solve for x:

x = 240/32

Simplifying the fraction:

x = 7.5

Now that we have x, we can substitute it back into one of the original equations. Let's use the first equation:

4x - 7y = 23

Substituting x with 7.5:

4(7.5) - 7y = 23

Multiplying:

30 - 7y = 23

To isolate y, we subtract 30 from both sides:

-7y = 23 - 30

Simplifying:

-7y = -7

Finally, divide both sides by -7 to solve for y:

y = (-7) / (-7)

Simplifying:

y = 1

Therefore, the solution to the system of equations is x = 7.5 and y = 1.

To solve these equations using the elimination method, we need to eliminate one variable so that we can find the value of the other variable. Let's start by eliminating either x or y.

We notice that the coefficients of y in both equations are the opposite of each other. This makes it convenient to eliminate y.

To do this, we can multiply both sides of the second equation by 7 to make the coefficients of y in both equations equal:

7 * (3y) = 7 * (-6x + 33)
21y = -42x + 231

Now, we can add the two equations together to eliminate y:

(4x - 7y) + (21y) = 23 + (-42x + 231)

Simplifying this equation gives us:

4x - 7y + 21y = 23 - 42x + 231
4x + 14y = -42x + 254

Next, we want to eliminate x. To do this, we can multiply both sides of the first equation by 42 to make the coefficients of x in both equations equal:

42 * (4x - 7y) = 42 * 23
168x - 294y = 966

Now, we can add the two equations together:

(168x - 294y) + (4x + 14y) = 966 + (-42x + 254)

Simplifying this equation gives us:

168x - 294y + 4x + 14y = 966 - 42x + 254
172x - 280y = -42x + 1220

We now have a new equation:

172x - 280y = -42x + 1220

But this equation is not enough to find the values of x and y. We need another equation.

Ensure we have not made an error during the elimination process. Check the original equations and the steps followed to see if any mistakes were made.

If there is another equation provided or we may have made an error, please provide the third equation or check the steps taken to solve the problem.

Elimination

4x-7y=23
3y=-6x+33

4x -7y = 23
6x + 3y = 33

12x -21y = 69
42x + 21y = 231

54x = 300

x = 300/54

y = -1/9