Estimate the solution to the system of these linear equations based on the graph.

Question

y=5x+10
y
=
5
x
+
10

y=−2x+3
y
=
−
2
x
+
3

(1 point)
Responses

(−1, 5)
(
−
1
,

5
)
left parenthesis negative 1 comma 5 right parenthesis

(−1,−5)
(
−
1
,
−
5
)
left parenthesis negative 1 comma negative 5 right parenthesis

(5,−1)
(
5
,
−
1
)
left parenthesis 5 comma negative 1 right parenthesis

(1, 5)

Answer 1

To find the solution to the system of equations, we need to identify the point where the two lines intersect.

The equations given are:

1. \( y = 5x + 10 \)
2. \( y = -2x + 3 \)

To find the intersection point, we set the equations equal to each other:

\[ 5x + 10 = -2x + 3 \]

Now, solve for \( x \):

1. Add \( 2x \) to both sides: \[ 5x + 2x + 10 = 3 \] \[ 7x + 10 = 3 \]

2. Subtract \( 10 \) from both sides: \[ 7x = 3 - 10 \] \[ 7x = -7 \]

3. Divide by \( 7 \): \[ x = -1 \]

Now, substitute \( x = -1 \) back into one of the original equations to find \( y \). We can use either equation, but let's use the second equation:

\[ y = -2(-1) + 3 \] \[ y = 2 + 3 \] \[ y = 5 \]

So, the intersection point is \((-1, 5)\).

Based on the options given, the correct response is:

\((-1, 5)\) (which corresponds to the first option).

Answer 2

Question
What is the last step to solving a system of equations?(1 point)
Responses

Make a table of solutions of the linear equations.
Make a table of solutions of the linear equations.

Estimate the intersection point.
Estimate the intersection point.

Graph the lines.
Graph the lines.

Check the answer.

Answer 3

The last step to solving a system of equations typically involves verifying that the solution is correct. This is done by substituting the solution back into the original equations to ensure that it satisfies both equations.

Therefore, the correct response is:

Check the answer.

Answer 4

Estimate the solution to the system of these linear equations based on the graph.

y=−5x+7
y
=
−
5
x
+
7

y=−2x+10
y
=
−
2
x
+
10
(1 point)
Responses

(−1,−12)
(
−
1
,
−
12
)
left parenthesis negative 1 comma negative 12 right parenthesis

(−1, 12)
(
−
1
,

12
)
left parenthesis negative 1 comma 12 right parenthesis

(1,−12)
(
1
,
−
12
)
left parenthesis 1 comma negative 12 right parenthesis

(12,−1)

Answer 5

To estimate the solution to the system of equations based on the graphs provided, we first need to find the intersection point of the two lines defined by the equations:

1. \( y = -5x + 7 \)
2. \( y = -2x + 10 \)

To find the intersection point, we set the two equations equal to each other:

\[ -5x + 7 = -2x + 10 \]

Now, solve for \( x \):

1. Add \( 5x \) to both sides: \[ 7 = 3x + 10 \]

2. Subtract \( 10 \) from both sides: \[ 7 - 10 = 3x \] \[ -3 = 3x \]

3. Divide by \( 3 \): \[ x = -1 \]

Now, substitute \( x = -1 \) back into one of the original equations to find \( y \). We can use the second equation:

\[ y = -2(-1) + 10 \] \[ y = 2 + 10 \] \[ y = 12 \]

Thus, the intersection point of the two lines is \((-1, 12)\).

Based on the response options given, the correct answer is:

(−1, 12) (which corresponds to the second option).