Find the solution of the system of equations.

Question

3, x, plus, 3, y, equals, 42
3x+3y=
42
x, minus, 3, y, equals, minus, 22
x−3y=
−22

Answer 1

To find the solution of the system of equations, we can use the method of substitution or elimination.

Method 1: Substitution
From the first equation, we have 3x + 3y = 42. We can isolate x by subtracting 3y from both sides:

3x = 42 - 3y
x = (42 - 3y) / 3
x = 14 - y

Now we substitute this expression for x into the second equation:

(14 - y) - 3y = -22
14 - 4y = -22
Subtract 14 from both sides:
-4y = -36
Divide both sides by -4:
y = 9

Now we substitute this value of y back into the expression for x:

x = 14 - y
x = 14 - 9
x = 5

Therefore, the solution to the system of equations is x = 5 and y = 9.

Method 2: Elimination
We can eliminate one variable by adding or subtracting the two equations. Let's start by eliminating y.

Multiply the second equation by 3 to make the y terms cancel out:

3(x - 3y) = 3(-22)
3x - 9y = -66

Now we can add this equation to the first equation:

3x + 3y + (3x - 9y) = 42 + (-66)
6x - 6y = -24

Divide both sides of this equation by 6:

x - y = -4

Now subtract this equation from the first equation:

3x + 3y - (x - y) = 42 - (-4)
2x + 4y = 46

Divide both sides of this equation by 2:

x + 2y = 23

Now we have a system of two equations:

x - y = -4
x + 2y = 23

Multiplying the first equation by 2, we can eliminate x:

2(x - y) = 2(-4)
2x - 2y = -8

Subtract this equation from the second equation:

(x + 2y) - (2x - 2y) = 23 - (-8)
-3x + 4y = 31

Now we have a new equation:

-3x + 4y = 31

Multiply the equation x + 2y = 23 by 3:

3(x + 2y) = 3(23)
3x + 6y = 69

Add this equation to -3x + 4y = 31:

3x + 6y + (-3x + 4y) = 69 + 31
10y = 100

Divide both sides by 10:

y = 10

Now substitute this value of y back into the equation x + 2y = 23:

x + 2(10) = 23
x + 20 = 23
Subtract 20 from both sides:
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 10.