Find the solution of the system of equations.

Question

minus, 3, x, minus, 7, y, equals, 5
−3x−7y=
5
15, x, plus, 6, y, equals, 33
15x+6y=
33

Answer 1

The system of equations is:

-3x - 7y = 5
15x + 6y = 33

To solve this system, we can use the method of substitution or elimination.

Method of Substitution:
1. Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
-3x - 7y = 5
-3x = 5 + 7y
x = (5 + 7y)/(-3)

2. Substitute this expression for x into the second equation.
15x + 6y = 33
15((5 + 7y)/(-3)) + 6y = 33
Multiply both sides of the equation by -3 to eliminate the fraction:
-45(5 + 7y) + 18y = -99
-225 - 315y + 18y = -99
Combine like terms:
-297y = 126
Divide both sides by -297:
y = -126/297
y = -14/33

3. Substitute the value of y into the expression for x.
x = (5 + 7(-14/33))/(-3)
x = (5 - 98/33)/(-3)
x = (15/3 - 98/33)/(-3)
x = (165/33 - 98/33)/(-3)
x = (67/33)/(-3)
x = -67/99

The solution to the system of equations is x = -67/99 and y = -14/33.

Method of Elimination:
1. Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations equal:
-15x - 35y = 25
45x + 18y = 99

2. Add the two equations together to eliminate x:
(-15x - 35y) + (45x + 18y) = 25 + 99
-15x + 45x - 35y + 18y = 124
30x - 17y = 124

3. Solve this equation for one variable in terms of the other variable.
Let's solve for x:
30x - 17y = 124
30x = 124 + 17y
x = (124 + 17y)/30

4. Substitute this expression for x into either of the original equations to solve for y.
Let's substitute into the first equation:
-3x - 7y = 5
-3((124 + 17y)/30) - 7y = 5
Multiply through by 30 to eliminate the fraction:
-30(124 + 17y) - 210y = 150
-3720 - 510y - 210y = 150
-720y = 3870
y = 3870/-720
y = -14/33

5. Substitute the value of y into the expression for x.
x = (124 + 17(-14/33))/30
x = (124 - 238/33)/30
x = (124 - 238/33)/30
x = (124/1 - 238/33)/30
x = (124*33 - 238)/33
x = (4092 - 238)/33
x = 3854/33
x = -67/99

Again, the solution to the system of equations is x = -67/99 and y = -14/33.