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Question

1. Solve the system of two equations using substitution.
y = 2 + 3x
4x - 3y = -16

Answer 1

First, we will substitute the value of y from the first equation into the second equation:

4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2

Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:

y = 2 + 3(2)
y = 2 + 6
y = 8

Therefore, the solution to the system of equations is x = 2 and y = 8.

Answer 2

2. Solve the system of equations.
2x + 6y = -18
x = 5y - 1

Answer 3

First, we will substitute the value of x from the second equation into the first equation:

2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1

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

x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the solution to the system of equations is x = -6 and y = -1.

Answer 4

3. Solve the system of equations.
3x + y = 2
7x - 4y = 30

Answer 5

To solve the system of equations, we will use the elimination method. First, we will multiply the first equation by 4 to eliminate y:

4(3x + y) = 4(2)
12x + 4y = 8

Now, we will add this modified first equation to the second equation:

12x + 4y + 7x - 4y = 8 + 30
19x = 38
x = 2

Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:

3(2) + y = 2
6 + y = 2
y = -4

Therefore, the solution to the system of equations is x = 2 and y = -4.

Answer 6

4. Solve the system of equations.
-4x + 6y = 38
x - 5y = -20

Answer 7

To solve this system of equations, we will use the elimination method. First, let's multiply the second equation by 4 to eliminate x:

4(x - 5y) = 4(-20)
4x - 20y = -80

Now, we will add this modified second equation to the first equation:

-4x + 6y + 4x - 20y = 38 - 80
-14y = -42
y = 3

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

x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5

Therefore, the solution to the system of equations is x = -5 and y = 3.

Answer 8

5. How many solution(s) does the system of equations have?
-5x + y = -18
10x + 2y = 36

Answer 9

To determine how many solutions this system of equations has, we first need to check if the lines represented by the two equations are parallel or coincidental. We can do this by checking if the coefficients of x and y in the two equations are proportional.

The first equation is: -5x + y = -18
The second equation is: 10x + 2y = 36

If we divide the first equation by -18 and the second equation by 36, we get:

-5x/-18 + y/-18 = 1
10x/36 + 2y/36 = 1

This simplifies to:

5x/18 - y/18 = 1
5x/18 + y/18 = 1

As we can see, the two equations have the same slope and y-intercept, hence they are coincidental and represent the same line. Therefore, the system of equations has infinitely many solutions.