Question

Solve the system of two equations using substitution. y=2+3x 4x−3y=−16 (1 point) Responses (2, 8) left parenthesis 2 comma 8 right parenthesis (−2, 4) left parenthesis negative 2 comma 4 right parenthesis (−2, −4) left parenthesis negative 2 comma negative 4 right parenthesis (2, 10)

Answer 1

Solve the system of equations. 2x+6y=−18 x=5y−1 (1 point) Responses (−7.25, −1.25) left parenthesis negative 7.25 comma negative 1.25 right parenthesis (5.25, 1.25) left parenthesis 5.25 comma 1.25 right parenthesis (−6, −1) left parenthesis negative 6 comma negative 1 right parenthesis (4, 1)

Answer 2

Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses (2, −4) left parenthesis 2 comma negative 4 right parenthesis (12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis (−2, 8) left parenthesis negative 2 comma 8 right parenthesis (2, −2)

Answer 3

Solve the system of equations. −4x+6y=38 x−5y=−20 (1 point) Responses (−35, −3) left parenthesis negative 35 comma negative 3 right parenthesis (−5, 3) left parenthesis negative 5 comma 3 right parenthesis (5, 3) left parenthesis 5 comma 3 right parenthesis (35, −3)

Answer 4

How many solution(s) does the system of equations have? −5x+y=−18 10x−2y=36 (1 point) Responses two two infinite infinite one one none

Answer 5

I got an 100%! Thanks Mini Bot!

Answer 6

To solve the system of equations using substitution, we have:

1. \( y = 2 + 3x \)
2. \( 4x - 3y = -16 \)

We can substitute the expression for \( y \) from the first equation into the second equation:

Substituting \( y \) into the second equation:

\[
4x - 3(2 + 3x) = -16
\]

Now, distribute the -3:

\[
4x - 6 - 9x = -16
\]

Combine like terms:

\[
-5x - 6 = -16
\]

Now, add 6 to both sides:

\[
-5x = -10
\]

Dividing both sides by -5 gives:

\[
x = 2
\]

Now that we have \( x \), 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:

\[
(x, y) = (2, 8)
\]

Thus, the answer is:

\((2, 8)\)

Answer 7

To solve the system of equations:

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

We can use substitution. From the second equation, we have \( x \) expressed in terms of \( y \):

\[
x = 5y - 1
\]

Now, we can substitute this expression for \( x \) into the first equation:

\[
2(5y - 1) + 6y = -18
\]

Distributing the \( 2 \):

\[
10y - 2 + 6y = -18
\]

Combine like terms:

\[
16y - 2 = -18
\]

Now, add \( 2 \) to both sides:

\[
16y = -16
\]

Dividing both sides by \( 16 \):

\[
y = -1
\]

Now, substitute \( y = -1 \) back into the equation for \( x \):

\[
x = 5(-1) - 1 = -5 - 1 = -6
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-6, -1)
\]

So, the answer is:

\((-6, -1)\)

Answer 8

To solve the system of equations:

1. \( 3x + y = 2 \)
2. \( 7x - 4y = 30 \)

We can use substitution or elimination. Here, let's use substitution by solving the first equation for \( y \):

\[
y = 2 - 3x
\]

Now, we can substitute this expression for \( y \) into the second equation:

\[
7x - 4(2 - 3x) = 30
\]

Distributing the \(-4\):

\[
7x - 8 + 12x = 30
\]

Combine like terms:

\[
19x - 8 = 30
\]

Now, add \( 8 \) to both sides:

\[
19x = 38
\]

Dividing both sides by \( 19 \):

\[
x = 2
\]

Now that we have \( x \), we can substitute it back into the expression for \( y \):

\[
y = 2 - 3(2) = 2 - 6 = -4
\]

So the solution to the system of equations is:

\[
(x, y) = (2, -4)
\]

Thus, the answer is:

\((2, -4)\)

Answer 9

To solve the system of equations:

1. \( -4x + 6y = 38 \)
2. \( x - 5y = -20 \)

We can use the substitution or elimination method. Here, I'll use the elimination method for this example.

### Step 1: Rearrange the second equation
First, we can isolate \( x \) in the second equation:

\[
x = 5y - 20
\]

### Step 2: Substitute into the first equation
Now we'll substitute \( x \) from the second equation into the first equation:

\[
-4(5y - 20) + 6y = 38
\]

### Step 3: Distribute and simplify
Distributing \(-4\):

\[
-20y + 80 + 6y = 38
\]

Combine the \( y \) terms:

\[
-14y + 80 = 38
\]

### Step 4: Solve for \( y \)
Now, subtract \( 80 \) from both sides:

\[
-14y = 38 - 80
\]
\[
-14y = -42
\]

Now, divide by \(-14\):

\[
y = 3
\]

### Step 5: Substitute back to find \( x \)
Now that we have \( y \), we can substitute \( y = 3 \) back into the equation for \( x \):

\[
x = 5(3) - 20
\]
\[
x = 15 - 20
\]
\[
x = -5
\]

### Solution
Thus, the solution to the system of equations is:

\[
(x, y) = (-5, 3)
\]

So, the answer is:

\((-5, 3)\)

Answer 10

To determine how many solutions the system of equations has, we need to analyze the equations:

1. \( -5x + y = -18 \)
2. \( 10x - 2y = 36 \)

Let's first manipulate these equations to see if they are equivalent or consistent.

### Step 1: Rewrite the equations
We can rearrange the first equation:

\[
y = 5x - 18
\]

For the second equation, we can rewrite it in a similar form. We can isolate \( y \):

\[
10x - 2y = 36
\]
\[
-2y = -10x + 36
\]
\[
y = 5x - 18
\]

### Step 2: Compare the two equations
Both equations can be rewritten as:

\[
y = 5x - 18
\]

Since both equations are identical, they represent the same line. This means that every point on this line is a solution to the system of equations.

### Conclusion
The system of equations has **infinitely many solutions**.

Therefore, the answer is **infinite**.

Answer 11

That's fantastic! 🎉 Congratulations on your perfect score! If you have any more questions or need further help, feel free to ask. Keep up the great work!