6. y = 2x - 1 and y = x + 3
***A. (4,7)
B. (7, 4)
C. (-7, -4)
D. infinite solutions
7. y = 4x and y + x = 5
A. (-4, 1)
B. (1, 4)
C. (-3, 2)
***D. (2,3)
8. What will the graph look like for a system of equations that has no solution?
A. The lines will be perpendicular.
***B. The lines will cross at one point
C. Both equations will form the same line
D. The lines will be parallel.
#6 ok
#7 ?!?!!?
y = 4x and y + x = 5
4x+x = 5
x=1
...
#8 ?!?!?!?
NO SOLUTION
They never cross. Parallel
To solve systems of equations, we need to find the values of x and y that satisfy both equations. Here's how to solve each of the given systems and find the correct answer:
6. To find the solution for this system, we can set the two equations equal to each other:
2x - 1 = x + 3
We can subtract x from both sides:
2x - x - 1 = x - x + 3
x - 1 = 3
Now, we can add 1 to both sides:
x - 1 + 1 = 3 + 1
x = 4
Now that we have x = 4, we can substitute this value into either of the original equations to find the corresponding value of y. Let's use the equation y = 2x - 1:
y = 2(4) - 1
y = 8 - 1
y = 7
Therefore, the solution to this system of equations is (4,7). The correct answer is A.
7. For this system, we have two equations:
y = 4x
y + x = 5
To solve this system, we can substitute the expression for y from the first equation into the second equation:
4x + x = 5
Combining like terms, we get:
5x = 5
Dividing both sides by 5, we find:
x = 1
Substituting this value back into either of the original equations, let's use y = 4x:
y = 4(1)
y = 4
Therefore, the solution to this system of equations is (1,4). The correct answer is B.
8. If a system of equations has no solution, it means that the equations describe two lines that do not intersect. In other words, the lines are parallel.
Therefore, the correct answer to this question is D - the lines will be parallel.