Questions: Solve each system by graphing. 5) y=x+3, 2x+4y=4 6) y=2x+1 7) x+2y+4=2x-4y=22 8) 2x-y=4, 4x=2y+8

Solution Steps

Problem 5:

• $x-y=3 \implies y = x-3$
• $x+2y=8 \implies 2y=-x+8 \implies y=-\frac{1}{2}x + 4$

Problem 6:

• $y=3x+5$
• $y=3x+6$

Problem 7:

• $x+2y=6 \implies 2y=-x+6 \implies y=-\frac{1}{2}x + 3$
• $2x+4y=12 \implies 4y=-2x+12 \implies y=-\frac{1}{2}x + 3$

Problem 5: The solution is the point where the lines intersect, which is $(3,-2)$.

Problem 6: These lines have the same slope but different y-intercepts, meaning they are parallel and will never intersect. Therefore, there is no solution.

Problem 7: These equations represent the same line, meaning there are infinitely many solutions. Any point that satisfies one equation will also satisfy the other.

Final Answer