Solve the system of equations

4x - 8y = -36
-6x + y = 32
(_,_)

9 answers

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:

Multiply the second equation by 8 to make the coefficient of y equal to 8:

-6x + y = 32
-48x + 8y = 256

Now, add the two equations:

4x - 8y = -36
-48x + 8y = 256
-------------------
-44x = 220

Divide by -44 on both sides:

x = -5

Now substitute x back into one of the original equations to find y. Let's use the first equation:

4(-5) - 8y = -36
-20 - 8y = -36
-8y = -36 + 20
-8y = -16
y = 2

Therefore, the solution to the system of equations is:
x = -5
y = 2
sooo
The solution to the system of equations is:

x = -5
y = 2

Therefore, the solution to the system of equations is (-5, 2).
Solve the system of equations
6x - 3y = -6
9x - 3y = -18
(_,_)
To solve the system of equations:

6x - 3y = -6
9x - 3y = -18

We can see that the coefficients for y are the same in both equations. This means we can easily eliminate y by subtracting the first equation from the second equation:

(9x - 3y) - (6x - 3y) = -18 - (-6)
3x = -12
x = -4

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

6x - 3y = -6
6(-4) - 3y = -6
-24 - 3y = -6
-3y = -6 + 24
-3y = 18
y = -6

Therefore, the solution to the system of equations is:
x = -4
y = -6

So, the solution to the system of equations is (-4, -6).
Solve the system of equations
5x - 4y = -44
-x + 3y = 22
(_,_)
To solve the system of equations:

5x - 4y = -44
-x + 3y = 22

We can use the elimination method to solve this system.

To eliminate x, we'll multiply the second equation by 5:

-5x + 15y = 110

Now, add this modified equation to the first equation:

5x - 4y = -44
-5x + 15y = 110
-------------------
11y = 66
y = 6

Now that we have the value of y, we can substitute it back into the second equation to solve for x:

-x + 3(6) = 22
-x + 18 = 22
-x = 22 - 18
-x = 4
x = -4

Therefore, the solution to the system of equations is:
x = -4
y = 6

So, the solution to the system of equations is (-4, 6).
The Math Club sold slices of pizza, p , at a profit of $3 each and cans of soda, s , at $2 each to raise money for a trip. They sold 200 items and made a profit of $550. Write the pair of linear equations that model this situation.(1 point) Equation to represent the total number of items sold: = 200 Equation to represent the total profit: = 550
Let's define the variables:
Let p be the number of slices of pizza sold
Let s be the number of cans of soda sold
Given:
1. They sold 200 items in total: p + s = 200
2. They made a profit of $550: 3p + 2s = 550

Therefore, the pair of linear equations that model this situation is:
1. p + s = 200
2. 3p + 2s = 550

These two equations represent the total number of items sold and the total profit made by selling slices of pizza and cans of soda.