Solving Systems of Equations by Graphing Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
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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The intersection point is (-2, -1).
no
Apologies for the error. Let's solve the system of equations x - 5y = 3 and 3x - 2y = -4.
To find the solution, we can set up the system of equations:
x - 5y = 3
3x - 2y = -4
To solve this system, we can use either substitution or elimination method.
Let's use the elimination method to solve the system:
Multiply the first equation by 3 and the second equation by -1 to eliminate the x term:
3(x - 5y) = 3(3)
-1(3x - 2y) = -1(-4)
Simplifying, we get:
3x - 15y = 9
-3x + 2y = 4
Now, add the two equations together to eliminate the x term:
(3x - 15y) + (-3x + 2y) = 9 + 4
Simplifying, we get:
-13y = 13
Divide both sides by -13:
y = -1
Now, substitute the value of y back into one of the original equations to find x:
x - 5(-1) = 3
x + 5 = 3
x = 3 - 5
x = -2
So, the solution to the system of equations is x = -2, y = -1.
no its not
Solving Systems of Equations by Graphing Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items
Question
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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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)
(
)
The intersection point of the graphs is (2, 4).
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)
(
)
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