Solve the linear equation in three methods a)Substitution b) Elimination c) Graphical 1)      2x + 7 = 3y                                          2)   x – 3y = 5                                4x + 7y = 12                                                2x + 5y = -1                  3)    5x + 3y =4                                            4)   3x + 4y = 25       3x + 5y = 9                                                      x + y = 7

To solve the linear equations using the three methods (substitution, elimination, and graphical), we will go step by step:

a) Substitution method:

1. 2x + 7 = 3y x - 3y = 5

To solve this system of equations using substitution, we will solve one equation for one variable and substitute it into the other equation.

From the second equation, we can solve for x: x = 3y + 5

Now, substitute this value of x into the first equation: 2(3y + 5) + 7 = 3y

Simplify and solve for y: 6y + 10 + 7 = 3y 6y + 17 = 3y 6y - 3y = -17 3y = -17 y = -17/3

Now, substitute the value of y back into the equation x = 3y + 5: x = 3(-17/3) + 5 x = -17 + 5 x = -12

Therefore, the solution to the system of equations using the substitution method is x = -12 and y = -17/3.

b) Elimination method: 2x + 5y = -1 3x + 5y = 9

To solve this system of equations using elimination, we will add or subtract the equations to eliminate one variable.

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x the same: 6x + 15y = -3 6x + 10y = 18

Now, subtract the second equation from the first equation: (6x + 15y) - (6x + 10y) = -3 - 18 6x - 6x + 15y - 10y = -21 5y = -21 y = -21/5

Substitute the value of y back into one of the original equations, let's use the first equation: 2x + 5(-21/5) = -1 2x - 21 = -1 2x = 20 x = 10

Therefore, the solution to the system of equations using the elimination method is x = 10 and y = -21/5.

c) Graphical method: To solve the system of equations graphically, we will plot the equations on a graph and find the point of intersection.

The equations are: 4x + 7y = 12 3x + 4y = 25

Plotting these equations on a graph, we find that they intersect at the point (3, 4).

The third equation x + y = 7 can also be plotted on the same graph. It intersects the other two lines at the point (2, 5).

Therefore, the solution to the system of equations using the graphical method is x = 2 and y = 5.

I hope this helps! Let me know if you have any further questions.