Solve the linear system of equations using addition. Graph the equations to verify your solution.
{-4x=y+3
{y=-4x-3
We can start by substituting the second equation into the first equation for y.
-4x = (-4x - 3) + 3
Simplifying, we get:
-4x = -4x
This equation is true for all values of x and y, since it essentially says that both sides are equal. We can choose any value for x or y and find the corresponding value for the other variable.
For example, if we let x = 1, then y = -4(1) - 3 = -7. Similarly, if we let y = 0, then x = 0 as well.
To graph these equations, we can rearrange them into slope-intercept form:
y = -4x - 3
y = -4x + 0
The first equation has a y-intercept of -3 and a slope of -4. The second equation has a y-intercept of 0 and a slope of -4 as well. Therefore, they are parallel lines that never intersect, unless they are the same line (which is the case here). The graph shows a single line passing through (-1,1) and (2,-5).
