Question

What is the solution to the system of equations graphed below?

Answer 1

Answer: B. (-2,1)

Step-by-step explanation:

Hi, to answer this question we have to solve the system of equations:

y=1/2x+ 2  

y = -2x - 3

Multiplying the first equation by 4 and adding both equations:

4y = 2x +8

+

y = -2x - 3

---------------

5y = 5

y =5/5

y=1

Replacing the value of y in any equation:

y = -2x - 3

1 = -2x - 3

Solving for x:

2x =-3-1

2x=-4

x =-4/2

x =-2

So, the solution is  

x =-2; y = 1

The correct option is B. (-2,1)

Answer 2

Answer:

Option B) (-2,1) is correct.

Step-by-step explanation:

The given equations are, $y=1/2x+ 2 and y = -2x - 3$.

Let the point of intersection be (a,b).

Thus (a,b) satisfies both the equations.

$b=1/2a+ 2$

$b = -2a - 3$

subtracting both the equations we get,

$(\frac{5}{2})(x) = -5$

x = -2, now inserting this value in anyone of the equations,  

$y = -2(-2) -3 = 4-3 = 1$

Thus, the intersection point is (-2,1).