To find the intersection point of the two equations, we can solve the system of equations using any method such as substitution or elimination.
Let's solve the system of equations using the substitution method:
First, isolate one of the variables in one equation. We'll isolate x in the first equation:
x - 5y = 7
x = 7 + 5y
Now substitute this expression for x into the second equation:
3(7 + 5y) - 2y = -4
21 + 15y - 2y = -4
21 + 13y = -4
13y = -4 - 21
13y = -25
y = -25/13 ≈ -1.923
Now substitute this value of y back into the expression for x:
x = 7 + 5(-25/13) = 7 - (125/13) = (91 - 125)/13 = -34/13 ≈ -2.615
So the solution to the system of equations is (x, y) = (-34/13, -25/13) or approximately (-2.615, -1.923).
To graph the system of equations, we can plot the two lines and find their intersection point:
To graph the equation x - 5y = 7, we can rewrite it in slope-intercept form:
-5y = -x + 7
y = (1/5)x - 7/5
To graph the equation 3x - 2y = -4, we can rewrite it in slope-intercept form:
-2y = -3x - 4
y = (3/2)x + 2
Now we can plot the two lines on a coordinate plane:
The line for the equation y = (1/5)x - 7/5 has a y-intercept of -7/5 and a slope of 1/5, meaning that for every increase of 1 in x, y increases by 1/5.
The line for the equation y = (3/2)x + 2 has a y-intercept of 2 and a slope of 3/2, meaning that for every increase of 1 in x, y increases by 3/2.
The two lines intersect at the point (-34/13, -25/13).
Overall, the graphs of the system of equations and the solution to both equations are visually represented by the intersection point (-34/13, -25/13).
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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