Please help me solve:
y-x=5
2x-2y=10
&
5X+6y=14
-3y+x=7
The first set cannot be solved, the two lines represented in the equations are parallel, and have no solution.
The second set, the second equation tells us that x= 3y+7, put that in the first equation
5(3y+7)+6y=14
15y+6y=14-35 solve for y
21y=-21 21y/21=-21/21 y=-1
To solve the system of equations:
y - x = 5 -- (Equation 1)
2x - 2y = 10 -- (Equation 2)
Step 1: Solve Equation 1 for y
Rearrange Equation 1 to solve for y:
y = x + 5
Step 2: Substitute the value of y in Equation 2
Now we substitute the value of y from Equation 1 into Equation 2:
2x - 2(x + 5) = 10
Step 3: Solve for x
Distribute the -2 to both terms inside the parentheses:
2x - 2x - 10 = 10
Simplifying:
-10 = 10
This is a contradiction. The equation -10 = 10 is not true, which means there is no solution to this system of equations. The two lines representing the equations are parallel and never intersect.
Now let's move on to the second system of equations:
5x + 6y = 14 -- (Equation 1)
-3y + x = 7 -- (Equation 2)
Step 1: Solve Equation 2 for x
Rearrange Equation 2 to solve for x:
x = 3y + 7
Step 2: Substitute the value of x in Equation 1
Now we substitute the value of x from Equation 2 into Equation 1:
5(3y + 7) + 6y = 14
Step 3: Solve for y
Distribute the 5 to both terms inside the parentheses:
15y + 35 + 6y = 14
Combine like terms:
21y + 35 = 14
Subtract 35 from both sides:
21y = 14 - 35
21y = -21
Divide both sides by 21:
y = -1
Step 4: Substitute the value of y into Equation 2
Now that we have the value of y, we substitute it into Equation 2 to solve for x:
x = 3(-1) + 7
x = -3 + 7
x = 4
Thus, the solution to the second system of equations is x = 4 and y = -1.