se a graphing calculator or Excel to find the solution of the system of equations. (If the system is dependent, enter DEPENDENT. If there is no solution, enter NO SOLUTION.)
5x + 3y = 2
3x + 7y = −4
So graph the two lines. Do they cross? If so, they are consistent, and you can read the solution where the lines cross.
If the lines do not cross, there is no solution.
To find the solution to the system of equations using a graphing calculator or Excel, we can input the equations into a graphing calculator or Excel and solve for the values of x and y that satisfy both equations.
Using a graphing calculator:
1. Input the first equation, 5x + 3y = 2, into the graphing calculator.
2. Input the second equation, 3x + 7y = -4, into the graphing calculator.
3. Use the graphing calculator's function to find the intersection point or points of the two equations.
4. The coordinates of the intersection point(s) are the solution(s) to the system of equations.
Using Excel:
1. Open Excel and create a new spreadsheet.
2. Enter the first equation, 5x + 3y = 2, into two adjacent cells. For example, enter "5" into cell A1, "3" into cell B1, "=2" into cell C1, and "=A1*x + B1*y" into cell D1.
3. Enter the second equation, 3x + 7y = -4, into two adjacent cells below the first equation. For example, enter "3" into cell A2, "7" into cell B2, "=-4" into cell C2, and "=A2*x + B2*y" into cell D2.
4. Use Excel's solver function to find the values of x and y that make both equations equal to zero. This will give the solution(s) to the system of equations.
Once you have solved the equations using a graphing calculator or Excel, you will obtain the solution(s) to the system of equations.
To solve the system of equations using a graphing calculator or Excel, follow these steps:
1. Open a graphing calculator or Excel spreadsheet.
2. Enter the coefficients of the variables and constants for the first equation. In this case, enter 5 for x, 3 for y, and 2 for the constant term.
3. Enter the coefficients of the variables and constants for the second equation. In this case, enter 3 for x, 7 for y, and -4 for the constant term.
4. Use the graphing capabilities of the calculator or Excel to plot the lines represented by each equation.
5. Look for the point of intersection of the two lines. This point represents the solution to the system of equations.
6. If there is a point of intersection, read off the values of x and y at that point. These values are the solution to the system of equations.
7. If the lines are parallel and never intersect, the system of equations has no solution. In this case, enter "NO SOLUTION."
8. If the lines overlap and are identical, meaning they have infinitely many points of intersection, the system of equations is dependent. In this case, enter "DEPENDENT."