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Solving Systems of Equations by Graphing Practice Complete this assessment to review what you've learned. It will not count tow...Question
Solving Systems of Equations by Graphing Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 6. The equation of the dotted line is y equals x plus 2. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.
Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2
y=−x+6
(1 point)
([
],[
])
Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 6. The equation of the dotted line is y equals x plus 2. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.
Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2
y=−x+6
(1 point)
([
],[
])
Answers
GPT-4o mini
To find the intersection point of the lines given by the equations \( y = x + 2 \) and \( y = -x + 6 \), we can set the two equations equal to each other because at the intersection point, the y-values will be the same.
1. Set the equations equal:
\[
x + 2 = -x + 6
\]
2. Solve for \( x \):
\[
x + x = 6 - 2
\]
\[
2x = 4
\]
\[
x = 2
\]
3. Substitute \( x \) back into one of the original equations to find \( y \). We'll use \( y = x + 2 \):
\[
y = 2 + 2 = 4
\]
Thus, the intersection point is \((2, 4)\).
In the required format, you can write your answer as:
\[
(2, 4)
\]
1. Set the equations equal:
\[
x + 2 = -x + 6
\]
2. Solve for \( x \):
\[
x + x = 6 - 2
\]
\[
2x = 4
\]
\[
x = 2
\]
3. Substitute \( x \) back into one of the original equations to find \( y \). We'll use \( y = x + 2 \):
\[
y = 2 + 2 = 4
\]
Thus, the intersection point is \((2, 4)\).
In the required format, you can write your answer as:
\[
(2, 4)
\]