Use the graph to answer the question, x - 5y = 7 and 3x - 2y = -4
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 can use the substitution method.
First, let's solve for x in the first equation:
x - 5y = 7
x = 7 + 5y
Now we substitute this expression for x into the second equation:
3(7 + 5y) - 2y = -4
21 + 15y - 2y = -4
13y = -25
y = -25/13
Now that we have found the value of y, we can substitute it back into the first equation to find the value of x:
x = 7 + 5(-25/13)
x = 7 - 125/13
x = 56/13
Therefore, the solution to the system of equations is x = 56/13 and y = -25/13.
can you simplify them
Sure, I will simplify the fractions for you:
x = 56/13 = 4 4/13
y = -25/13 = -1 12/13
So, the simplified solution to the system of equations is x = 4 4/13 and y = -1 12/13.
can you simplify them more
Sure, I can further simplify the fractions for you:
x = 4 4/13 = 4.3077 (rounded to four decimal places)
y = -1 12/13 = -1.9231 (rounded to four decimal places)
Therefore, the simplified solution to the system of equations is x ≈ 4.3077 and y ≈ -1.9231.