Solving systems of equations quiz part 1

Answer 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).