Question

1J

15 Find the solution to the following system of
equations:
x + 2y = -1
2x – 3y = 5
A. (-7,3)
B. (1, - 1)
C. (5. – 3)
D. (13. – 7)

Answer 1

Answer: B

Explanation:

(1) + 2(-1) = -1

(multiplying the negative 1 turns the 2 into a negative)

1 - 2 = -1

-1 = -1

TRUE

2(1) - 3(-1) = 5

(multiplying a negative and a negative makes a positive, -3 x -1 =3)

2 + 3 = 5

5=5

TRUE

Answer 2

(1,-1)

Explanation:

We can solve the system by using substitution.

However in order for this to work we must make x the subject in the first equation.

We can do this by simply subtracting 2y from both sides

x + 2y = -1

subtract 2y from both sides

x + 2y - 2y = -1 - 2y

simplify

x = -2y - 1

now that we have made x the subject in one of the equations we can plug in (or substitute) the value of x into the other equation

2x – 3y = 5

We know that x = -2y - 1

* substitute value of x *

2(-2y - 1) - 3y = 5

We can then solve for y

2(-2y - 1) - 3y = 5

Distribute the 2

-4y - 2 - 3y = 5

combine like terms -4y + -3y

-7y - 2 = 5

add 2 to both sides

-7y = 7

divide both sides by -7

y = -1

Now that we have found the value of y we can plug in the value of y into one of the equations and solve for x

x + 2y = -1

y = - 1

x + 2(-1) = -1

multiply 2 and -1

x + -2 = -1

add 2 to both sides

x = 1

So we have found that x = 1 and y = -1 therefore the solution to the system of equations is (1,-1)