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.
To find the solution to both equations, we need to find the point where the two lines intersect on the coordinate plane.
From the given equations:
1) x - 5y = 3
2) 3x - 2y = -4
Let's solve these equations simultaneously:
1) x - 5y = 3
x = 5y + 3
2) 3(5y + 3) - 2y = -4
15y + 9 - 2y = -4
13y + 9 = -4
13y = -13
y = -1
Now, substitute y = -1 into the equation x = 5y + 3:
x = 5(-1) + 3
x = -5 + 3
x = -2
Therefore, the solution to the system of equations x−5y=7 and 3x−2y=−4 is x = -2 and y = -1.
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 (
).