To find the solution to the system of two linear equations x - 5y = 7 and 3x - 2y = -4, we can solve the system using the method of substitution or elimination.
Method 1: Substitution
First, we solve one of the equations for x or y, then substitute that expression into the other equation to solve for the other variable.
From the first equation:
x = 7 + 5y
Now, substitute x into the second equation:
3(7 + 5y) - 2y = -4
21 + 15y - 2y = -4
13y = -25
y = -25/13
Now, substitute y back into x = 7 + 5y to find x:
x = 7 + 5(-25/13)
x = 7 - 125/13
x = 66/13
Therefore, the solution to the system of equations is:
x = 66/13
y = -25/13
Method 2: Graphing
We can also graph the equations on a Cartesian plane to find the intersection point which represents the solution to the system.
The graphs of the two equations x - 5y = 7 and 3x - 2y = -4 are two straight lines. By graphing these two lines, we can visually identify their intersection point.
Upon graphing, the intersection point of the two lines is (x = 66/13, y = -25/13). This confirms the solution obtained using the substitution method.
Therefore, the solution to the system of equations x - 5y = 7 and 3x - 2y = -4 is:
x = 66/13
y = -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.
The intersection point is (__)
3 answers
What is the intersection point?
The intersection point of the system of equations x - 5y = 7 and 3x - 2y = -4 is (x = 66/13, y = -25/13).