Question

Graph the following system of equation
y= 3x + 11
y= -4x + 4

Answer 1

These equations describe two lines that intersect at the point (-1, 8), one of them with a slope of 3, the other with a slope of -4.

Explanation:

We can find the point where these two lines intersect by taking one of the equations, solving it for x, and substituting it into the other equation.

`y = -4x + 4\\-4x = y - 4\\4x = 4 - y\\x = 1 - (y)/(4) \\\\y = 3x + 11\\y = 3(1 - (y)/(4)) + 11\\y = 3 - (3y)/(4) + 11\\y + (3y)/(4) = 3 + 11\\(4y)/(4) + (3y)/(4) = 14\\(7y)/(4) = 14\\y = (4)/(7) * 14\\y = 4 * (14)/(7)\\y = 4 * 2\\y = 8`

Now we can plug that into our first equation to find x

`x = 1 - \frac{y}[4}\\x = 1 - \frac{8}[4}\\\\x = 1 - 2\\x = -1`

So these lines intersect at the point (-1, 8), one of them with a slope of 3, the other with a slope of -4

Answer 2

Explanation: