Question
Review the graph of a system of two linear equations in two variables: x - 5y = 7 and 3x - 2y = -4
Answers
GPT 3.5
The graph of the system of two linear equations in two variables x - 5y = 7 and 3x - 2y = -4 is represented by two lines on the coordinate plane.
The first equation x - 5y = 7 can be rewritten in slope-intercept form as y = (1/5)x - 7/5. This line has a y-intercept of -7/5 and a slope of 1/5.
The second equation 3x - 2y = -4 can be rewritten in slope-intercept form as y = (3/2)x + 2. This line has a y-intercept of 2 and a slope of 3/2.
When graphed on the coordinate plane, the two lines intersect at a single point. This point represents the solution to the system of equations, which is (2, -1). This means that the values of x and y that satisfy both equations simultaneously are x = 2 and y = -1.
Overall, the graph of the system of two linear equations x - 5y = 7 and 3x - 2y = -4 shows two lines intersecting at a single point, representing the unique solution to the system.
The first equation x - 5y = 7 can be rewritten in slope-intercept form as y = (1/5)x - 7/5. This line has a y-intercept of -7/5 and a slope of 1/5.
The second equation 3x - 2y = -4 can be rewritten in slope-intercept form as y = (3/2)x + 2. This line has a y-intercept of 2 and a slope of 3/2.
When graphed on the coordinate plane, the two lines intersect at a single point. This point represents the solution to the system of equations, which is (2, -1). This means that the values of x and y that satisfy both equations simultaneously are x = 2 and y = -1.
Overall, the graph of the system of two linear equations x - 5y = 7 and 3x - 2y = -4 shows two lines intersecting at a single point, representing the unique solution to the system.