Use the image to answer the question.
A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3.
Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4 . Find the solution to both equations.
(1 point)
The intersection point is (
).
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9 answers
The intersection point is (3, 2).
wrong
Apologies for the mistake. Let's solve the system of equations to find the correct intersection point.
Given the equations:
1) x - 5y = 3
2) 3x - 2y = -4
To find the solution, we can use the method of substitution or elimination. Let's use the elimination method:
Multiplying equation 1) by 3 and equation 2) by 5 to eliminate the coefficients of x:
3(x - 5y) = 3 * 3
5(3x - 2y) = 5 * (-4)
Simplifying:
3x - 15y = 9
15x - 10y = -20
Now, let's subtract equation 1) from equation 2):
(15x - 10y) - (3x - 15y) = -20 - 9
15x - 10y - 3x + 15y = -29
12x + 5y = -29
Now, let's solve for x:
12x = -29 - 5y
x = (-29 - 5y)/12
Substitute this value of x back into equation 1):
(-29 - 5y)/12 - 5y = 3
-29 - 5y - 60y = 36
-65y = 36 + 29
-65y = 65
y = -1
Now, substitute this value of y back into the equation 1):
x - 5(-1) = 3
x + 5 = 3
x = 3 - 5
x = -2
So, the correct intersection point of the equations is (-2, -1).
Given the equations:
1) x - 5y = 3
2) 3x - 2y = -4
To find the solution, we can use the method of substitution or elimination. Let's use the elimination method:
Multiplying equation 1) by 3 and equation 2) by 5 to eliminate the coefficients of x:
3(x - 5y) = 3 * 3
5(3x - 2y) = 5 * (-4)
Simplifying:
3x - 15y = 9
15x - 10y = -20
Now, let's subtract equation 1) from equation 2):
(15x - 10y) - (3x - 15y) = -20 - 9
15x - 10y - 3x + 15y = -29
12x + 5y = -29
Now, let's solve for x:
12x = -29 - 5y
x = (-29 - 5y)/12
Substitute this value of x back into equation 1):
(-29 - 5y)/12 - 5y = 3
-29 - 5y - 60y = 36
-65y = 36 + 29
-65y = 65
y = -1
Now, substitute this value of y back into the equation 1):
x - 5(-1) = 3
x + 5 = 3
x = 3 - 5
x = -2
So, the correct intersection point of the equations is (-2, -1).
Use the image to answer the question.
A coordinate plane with four quadrants shows the x-axis ranging from negative 10 to 10 in increments of 1 and the y-axis ranging from negative 5 to 15 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals x plus 5. The equation of the dotted line is 4 x plus 3 y equals 15. The intersection point of both lines is shown at 0 on the x-axis and positive 5 on the y-axis.
Review the graphs of a system of two linear equations in two variables: 4x+3y=15 and y=x+5. Find the solution to both equations.
(1 point)
The intersection point is (
).
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page 16 of 17
A coordinate plane with four quadrants shows the x-axis ranging from negative 10 to 10 in increments of 1 and the y-axis ranging from negative 5 to 15 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals x plus 5. The equation of the dotted line is 4 x plus 3 y equals 15. The intersection point of both lines is shown at 0 on the x-axis and positive 5 on the y-axis.
Review the graphs of a system of two linear equations in two variables: 4x+3y=15 and y=x+5. Find the solution to both equations.
(1 point)
The intersection point is (
).
Skip to navigation
page 16 of 17
The intersection point is (0, 5).
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)
(
)
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page 16 of 17
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)
(
)
Skip to navigation
page 16 of 17
The estimated intersection point of the graphs of the linear equations y = x + 2 and y = -x + 6 is (2, 4).
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 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 7. The equation of the dotted line is y equals 4 x minus 3. The lines intersect at left parenthesis 2 comma 5 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+7
y=4x−3
(1 point)
(
)
Skip to navigation
page 16 of 17
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 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 7. The equation of the dotted line is y equals 4 x minus 3. The lines intersect at left parenthesis 2 comma 5 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+7
y=4x−3
(1 point)
(
)
Skip to navigation
page 16 of 17
The estimated intersection point of the graphs of the linear equations y = -x + 7 and y = 4x - 3 is approximately (2, 5).