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 (-2,-1).
The intersection point is (-2, -1).
To find the solution to both equations, we need to find the coordinates of the intersection point of the two lines.
The given equations are:
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 substitution method to solve the equations.
From the first equation (1), we can isolate x:
x = 3 + 5y
Substitute this value of x in the second equation (2):
3(3 + 5y) - 2y = -4
Simplify the equation:
9 + 15y - 2y = -4
13y + 9 = -4
Subtract 9 from both sides:
13y = -4 - 9
13y = -13
Divide both sides by 13:
y = -13/13
y = -1
Now substitute this value of y back into the first equation (1):
x - 5(-1) = 3
x + 5 = 3
x = 3 - 5
x = -2
So, the intersection point of the two lines is (-2, -1).