Question

The system of equations shown below is graphed on a coordinate grid:

4y + x = 4
2y - X= 8
Which statement is true about the coordinates of the point that is the solution to the system of equations?
a. it is (2,5) and lies on both lines,
b. It is (-4, 2) and lies on both lines.
c. It is (2, 5) and does not lie on either line.
d. It is (-4, 2) and does not lie on either line.

Answer 1

The solution to the system of equations is (-4, 2) and it lies on both lines.

Step-by-step explanation:

To find the solution to the system of equations, we can use the method of substitution. Starting with the first equation, 4y + x = 4, we can solve for x in terms of y: x = 4 - 4y. Now we can substitute this value of x into the second equation, 2y - (4 - 4y) = 8. Simplifying this equation, we get 10y - 4 = 8. Solving for y, we find y = 2. Substituting this value back into the first equation to solve for x, we get x = 4 - 4(2) = -4.

Therefore, the solution to the system of equations is (-4, 2). To determine if this point lies on both lines, we can substitute the x and y values into both equations. For the first equation, 4(2) - 4 = 4, and for the second equation, 2(2) - (-4) = 8. Both equations are satisfied, so the statement that is true about the coordinates of the solution is b. It is (-4, 2) and lies on both lines.