Solve the system of two equations using substitution.

Question

y = 2 + 3x

4x - 3y = - 16 (1 point)

Answer 1

By substitution, we can solve the system of equations as follows:

From the first equation, y = 2 + 3x.

We can substitute this value of y into the second equation:

4x - 3(2 + 3x) = - 16

Simplifying this equation:

4x - 6 - 9x = - 16

Combining like terms:

-5x - 6 = - 16

Adding 6 to both sides:

-5x = -10

Dividing both sides by -5:

x = 2

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

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

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

Answer 2

Solve the system of equations.

2x + 6y = - 18
x = 5y - 1 (1 point)

Answer 3

To solve the system of equations, we can substitute the value of x from the second equation into the first equation:

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

Simplifying this equation:

10y - 2 + 6y = -18

Combining like terms:

16y - 2 = -18

Adding 2 to both sides:

16y = -16

Dividing both sides by 16:

y = -1

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

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

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

Answer 4

Solve the system of equations.

3x + y = 2

7x - 4y = 30 (1 point)

Answer 5

We can solve the system of equations by substitution:

From the first equation, we have y = 2 - 3x.

We can substitute this value of y into the second equation:

7x - 4(2 - 3x) = 30

Simplifying this equation:

7x - 8 + 12x = 30

Combining like terms:

19x - 8 = 30

Adding 8 to both sides:

19x = 38

Dividing both sides by 19:

x = 2

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

3(2) + y = 2

6 + y = 2

Subtracting 6 from both sides:

y = -4

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

Answer 6

Solve the system of equations.
- 4x + 6y = 38.
x - 5y = - 20 (1 point)

Answer 7

To solve the system of equations, we can use either substitution or elimination method. Here, we will use the elimination method.

First, we can multiply the second equation by 4 to make the coefficients of x in both equations the same:

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

Now, we can subtract the first equation from this new equation:

(4x - 20y) - (-4x + 6y) = (-80) - (38)
4x - 20y + 4x - 6y = -80 - 38
8x - 20y - 6y = -118
8x - 26y = -118

Now we have a new equation:

8x - 26y = -118

Now, we can multiply the first equation by 26 to make the coefficients of y in both equations the same:

26(-4x + 6y) = 26(38)
-104x + 156y = 988

Now, we can subtract the second equation from this new equation:

(-104x + 156y) - (x - 5y) = 988 - (-20)
-104x + 156y - x + 5y = 988 + 20
-105x + 161y = 1008

Now we have another new equation:

-105x + 161y = 1008

So, the system of equations becomes:

8x - 26y = -118
-105x + 161y = 1008

Now we can solve this system of equations using the elimination method:

Multiply the first equation by -105 and the second equation by 8:

-105(8x - 26y) = -105(-118)
8(-105x + 161y) = 8(1008)

Simplifying these equations:

-840x + 2730y = 12390
-840x + 1288y = 8064

Now, we can subtract the first equation from the second equation to eliminate x:

(-840x + 1288y) - (-840x + 2730y) = 8064 - 12390
-840x + 1288y + 840x - 2730y = 8064 - 12390
-1442y = -4326

Dividing both sides by -1442:

y = 3

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

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

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

Answer 8

How many solution(s) does the system of equations have?

- 5x + y = - 18

10x - 2y = 36 (1 point)

one

none

infinite

two

Answer 9

The system of equations has infinite solutions. This is because the two equations are equivalent when multiplied by constant multiples.