Review the graphs of a system of two linear equations in two variables x-5y=7 and 2y=-4 Find the solution to both equations
To find the solution to the system of linear equations x - 5y = 7 and 2y = -4, we can first solve for y in the second equation:
2y = -4
y = -2
Now that we have found the value of y, we can substitute this value back into the first equation to solve for x:
x - 5(-2) = 7
x + 10 = 7
x = -3
Therefore, the solution to the system of linear equations x - 5y = 7 and 2y = -4 is x = -3 and y = -2.
Now let's review the graphs of these two equations:
1. Graph of x - 5y = 7:
To graph this equation, we can rewrite it in slope-intercept form:
y = (1/5)x - 7/5
The graph of this equation is a straight line with a slope of 1/5 and a y-intercept of -7/5.
2. Graph of 2y = -4:
To graph this equation, we can rewrite it as:
y = -2
The graph of this equation is a horizontal line at y = -2.
By looking at the graphs of these two equations, we can see that they intersect at the point (-3, -2), which is the solution we found earlier. This point represents the unique solution to the system of linear equations.