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 (
).
Skip to navigation
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).
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 (
).
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)
(
)
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
The estimated intersection point of the graphs of the linear equations y = -x + 7 and y = 4x - 3 is approximately (2, 5).
To find the solution to the equations, we need to find the coordinates of the intersection point of the two lines.
First, we need to set up the system of equations:
Equation 1: x - 5y = 7
Equation 2: 3x - 2y = -4
To find the solution, we can use the method of substitution or elimination. Let's use the method of substitution in this case.
From equation 1, we can isolate x:
x = 7 + 5y
Now we can substitute this expression for x into equation 2:
3(7 + 5y) - 2y = -4
Simplify the equation:
21 + 15y - 2y = -4
13y + 21 = -4
Subtract 21 from both sides:
13y = -25
Divide both sides by 13:
y = -25/13
Now substitute this value of y back into equation 1 to find x:
x - 5(-25/13) = 7
x + 125/13 = 7
Subtract 125/13 from both sides:
x = 7 - 125/13
To simplify the expression, we need to find a common denominator for 7 and 125/13:
x = (91/13 - 125/13)
x = -34/13
Therefore, the solution to the system of equations is x = -34/13 and y = -25/13.
The intersection point is (-34/13, -25/13).