Test: Simultaneous Equations - SAT MCQ

Multiply the first equation by 2 and subtract it from the second equation to eliminate y:
(2x + y) - (2x + 2y) = 9 - 10
-y = -1
y = 1
Substitute y in the first equation:
x + 2 = 5
x = 5 - 2
x = 3

We can solve this system using either the substitution or elimination method. Let's use the elimination method by multiplying the first equation by 3 and adding it to the second equation:

6x + 3y = 24
x - 3y = -5
7x = 19

So, x = 19/7. Substituting this value into the first equation, we get:

2(19/7) + y = 8

Solving for y, we get:

y = 18/7

Therefore, the answer is A) x = 19/7, y = 18/7.

We can use the substitution method by solving one equation for one variable and substituting it into the other equation. Solving the first equation for y, we get:

y = 3x - 7

Substituting this into the second equation, we get:

2x + 3(3x - 7) = 1

Simplifying and solving for x, we get:

x = 2

Substituting this value into the first equation, we get:

3(2) - y = 7

Solving for y, we get:

y = -1

Therefore, the answer is A) x = 2, y = -1.

We can solve this system of equations by using the elimination method. Multiply the first equation by 2,
we get 4x + 6y = 20.
This is the same as the second equation.
Therefore, the system has infinitely many solutions, and the correct answer is (d) No solution.

We can solve this system of equations by using the elimination method. Multiply the second equation by 3,
we get 6x - 9y = 15.
Adding this equation to the first equation,
we get 11x = 47. Solving for x,
we get x = 47/11.
Substituting x into the second equation,
we get y = -3/11.
The correct answer is (none of the above), x = 47/11, y = -3/11.

The given simultaneous equations have oppositely signed y terms.
By adding both equations, we can eliminate the y variable and solve for x.

Multiply the second equation by 2 to match the coefficients of x in both equations: 4x - 2y = 10.
Now add both equations: 8x = 18, and x = 9/4.