Question

Which system of equations has the same solution as the system below?

6
x
+
3
y
=
6x+3y=
 
 
−
66
−66
3
x
+
2
y
=
3x+2y=
 
 
−
35
−35


6
x
+
3
y
=
−
66
6x+3y=−66
3
x
−
4
y
=
70
3x−4y=70

6
x
+
3
y
=
−
66
6x+3y=−66
−
6
x
−
4
y
=
−
35
−6x−4y=−35

6
x
+
3
y
=
−
66
6x+3y=−66
−
6
x
+
2
y
=
70
−6x+2y=70

6
x
+
3
y
=
−
66
6x+3y=−66
−
6
x
−
4
y
=
70
−6x−4y=70

Answer 1

I did this on photomath and it said -66

Answer 2

The system of equations that has the same solution as the system 6·x + 3·y = -66, and 3·x + 2·y = -35 is the fourth option

• 6·x + 3·y = -66, and -6·x - 4·y = 70

The steps used to find the system of equation that has the same solution can be presented as follows;

The system of equation can be presented as follows;

6·x + 3·y = -66

3·x + 2·y = -35

Solving the above system of equations, we get;

y = (-66 - 6·x)/3

y = -22 - 2·x

3·x + 2 × (-22 - 2·x) = -35

-x - 44 = -35

-x = 44 - 35

x = -9

y = -22 - 2×(-9)

y = -4

The options are

• 6·x + 3·y = -66 and 3·x - 4·y = 70

• 6·x + 3·y = -66 and -6·x - 4·y = -35
• 6·x + 3·y = -66 and -6·x + 2·y = 70
• 6·x + 3·y = -66 and -6·x - 4·y = 70

Comparing the above options, we get;

The first equation in the system of equations in all the options are the same, 6·x + 3·y = -66, only the second equation in the fourth option that is a multiple of the second equation in the question

-6·x - 4·y = -2 × (3·x + 2·y)

70 = -2 × (-35)

The second equation in the fourth option is the product of the second equation in the question and a constant, which indicates that the second equations in the fourth option and the question are the same, and therefore, the system of equation in the fourth option has the same solution as the system of equation in the question