Solving systems of equations quiz part 1
1. Solve the following system of equations:
3x + 4y = 10
2x - 5y = -1
Solution:
To solve this system of equations, we can use the elimination method. We will multiply the first equation by 5 and the second equation by 4 to get:
15x + 20y = 50
8x - 20y = -4
Adding these two equations together, we get:
23x = 46
x = 2
Substituting x = 2 into either equation, we get:
3(2) + 4y = 10
6 + 4y = 10
y = 1
Therefore, the solution to the system of equations is (2, 1).
2. Solve the following system of equations:
2x - 3y = 8
4x + 5y = 12
Solution:
Again, we will use the elimination method. We will multiply the first equation by 5 and the second equation by 3 to get:
10x - 15y = 40
12x + 15y = 36
Adding these two equations together, we get:
22x = 76
x = 4
Substituting x = 4 into either equation, we get:
2(4) - 3y = 8
8 - 3y = 8
y = 0
Therefore, the solution to the system of equations is (4, 0).
3. Solve the following system of equations:
x + 2y = 5
3x - y = 7
Solution:
One way to solve this system of equations is to use substitution. Solve for x in the first equation:
x = 5 - 2y
Substitute this expression for x in the second equation:
3(5 - 2y) - y = 7
15 - 6y - y = 7
-7y = -8
y = 8/7
Substituting y = 8/7 into either equation, we get:
x + 2(8/7) = 5
x = 1/7
Therefore, the solution to the system of equations is (1/7, 8/7).
To solve a system of equations, follow these steps:
1. Identify the given equations: Write down the equations that form the system.
2. Choose a method: There are different methods to solve a system of equations, such as substitution, elimination, or graphing. Determine which method you will use based on the given equations.
3. Solve for one variable: Use the chosen method to solve for one variable in terms of the other variable in one of the equations. This will give you an expression that represents one variable in the system.
4. Substitute: Take the expression you found in step 3 and substitute it into the other equation(s) for the corresponding variable. This will create a new equation with only one variable.
5. Solve for the remaining variable: Solve the equation from step 4 for the remaining variable.
6. Check the solution: Substitute the values you found for the variables back into the original equations. If the values satisfy all the equations, then they are the correct solution. If not, go back and check your work.
Repeat these steps for each part of the quiz or the given systems of equations. Good luck!