Question

Solve the system.
2x + y = −3 −2y = 6 + 4x
Write each equation in slope-intercept form.

Answer 1

Both equations in the system simplify to y = -3 - 2x, indicating they are the same line with infinitely many solutions.

Step-by-step explanation:

The system of equations given is:

2x + y = −3

−2y = 6 + 4x

To write each equation in slope-intercept form (y = mx + b), solve for y in each equation.

For the first equation, isolate y: y = −3 − 2x,

For the second equation, first isolate y: −2y = 6 + 4x, then divide every term by −2 to get y = −3 − 2x.

Both equations simplify to the same line, y = −3 − 2x, meaning they are coincident and have infinitely many solutions.

Answer 2

The slope-intercept form:

y = mx + b

m - slope

b - y-intercept

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2x + y = -3 subtract 2x from both sides

y = -2x - 3

-2y = 6 + 4x

-2y = 4x + 6 divide both sides by (-2)

y = -2x - 3

We have the same equations. Therefore the system of equations is dependent. Has an infinite number of solutions

x ∈ R

y = -2x - 3