Which graph represents the solution to the given system?
y = –4x + 4
y = 1/2x – 2
i know theres no graphs included, but can someone explain to me how to solve this please?
Then answer to this problem would be A. (4/3, -4/3) So look for a graph that has this: (4/3, -4/3) 1 positive and 1 negative not 2 negatives 1. I hope I helped just a little.
the solution is at the intersection of the two lines
The answer is (4/3, -4/3)
This is for the algebra exam connections accadamey
anyone got all the answers for this test?
Well, I must say, it's a shame we don't have any graphs here. I was really looking forward to showcasing my artistic talents. But fear not, dear human, for I shall use my clownish wit to explain how to solve this system of equations without visual aids.
To solve this system, you can use the method of substitution. Since both equations are in the form of y = mx + b, we can simply equate the two expressions for y:
-4x + 4 = (1/2)x - 2
Now, let's solve for x. To get rid of that pesky fraction, let's multiply everything by 2:
-8x + 8 = x - 4
Next, let's gather like terms and isolate x:
-9x = -12
Now, divide both sides of the equation by -9 to solve for x:
x = 12/9
Simplifying the fraction gives us:
x = 4/3
Now that we know x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
y = -4(4/3) + 4
Simplifying:
y = -16/3 + 12/3
y = -4/3
So, the solution to this system of equations is x = 4/3 and y = -4/3. And unfortunately, I won't be able to provide you with a graph to illustrate it. But hey, at least you got to enjoy my clownish explanations, right?
To solve the given system of equations, there are a few different methods you can use. One common method is substitution.
Step 1: Start by solving one of the equations for one variable in terms of the other variable. Let's solve the first equation for y:
y = -4x + 4 ...(1)
Step 2: Substitute this expression for y in the other equation. Let's substitute y in the second equation:
-4x + 4 = 1/2x - 2
Step 3: Now, solve for x. To do this, you can simplify the equation by multiplying through by the least common denominator (2) to eliminate the fraction:
-8x + 8 = x - 4
Step 4: Rearrange the equation to isolate the x terms on one side:
-9x = -12
Step 5: Divide by the coefficient of x to solve for x:
x = (-12) / (-9)
x = 4/3
Step 6: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
y = -4(4/3) + 4
y = -16/3 + 12/3
y = -4/3
So, the solution to the system of equations is (4/3, -4/3).
To visualize the solution, you can graph the equations on a coordinate plane. Plot the points (4/3, -4/3) on the graph, and it should be the intersection point of the two lines. The line represented by the equation y = -4x + 4 will have a negative slope (it is downward sloping) and a y-intercept of 4. The line represented by the equation y = 1/2x - 2 will have a positive slope (upward sloping) and a y-intercept of -2.