Question

What is the solution to this system of equations?

A graph of the first and second quadrant consisting of a red line and blue line intersecting each other at a point at which the x intercept is -2 units and the y intercept is 4 units. Text that reads: y = x + 6. y = -0.5x + 3.
A. (–1, 2)
B. (4, –2)
C. (2, –1)
D. (–2, 4)

Answer 1

To find the solution to the system of equations represented by the given lines, we need to find the point where the lines intersect. The equations are \(y = x + 6\) and \(y = -0.5x + 3\).

Setting these equations equal to each other:

\[ x + 6 = -0.5x + 3 \]

Now, solve for \(x\):

\[ 1.5x = -3 \]

\[ x = -2 \]

Now that we have \(x = -2\), substitute this value back into one of the original equations. Let's use \(y = x + 6\):

\[ y = -2 + 6 \]

\[ y = 4 \]

So, the solution is \(x = -2, y = 4\). Therefore, the correct option is D. ((-2,4)).