Solution Pairs 101831

1. **State the problem:** We are given the equation $$y + 2x = 3$$ and two pairs of values: $$(2, -1)$$ and $$(4, -5)$$. We need to show that each pair is a solution to the equation and then graph these points to find another solution. 2. **Check if $$(2, -1)$$ is a solution:** Substitute $x=2$ and $y=-1$ into the equation: $$y + 2x = -1 + 2 \times 2 = -1 + 4 = 3$$ Since the left side equals the right side, $$(2, -1)$$ is a solution. 3. **Check if $$(4, -5)$$ is a solution:** Substitute $x=4$ and $y=-5$ into the equation: $$y + 2x = -5 + 2 \times 4 = -5 + 8 = 3$$ Since the left side equals the right side, $$(4, -5)$$ is a solution. 4. **Graph the equation and points:** Rewrite the equation in slope-intercept form: $$y + 2x = 3 \implies y = 3 - 2x$$ This is a straight line with slope $$-2$$ and y-intercept $$3$$. Plot the points $$(2, -1)$$ and $$(4, -5)$$ on the graph of $$y = 3 - 2x$$. 5. **Determine another solution:** Since the equation is linear, any point on the line $$y = 3 - 2x$$ is a solution. For example, choose $$x=0$$: $$y = 3 - 2 \times 0 = 3$$ So, $$(0, 3)$$ is another solution. **Final answer:** Both pairs $$(2, -1)$$ and $$(4, -5)$$ satisfy the equation $$y + 2x = 3$$. Another solution is $$(0, 3)$$, which lies on the line defined by the equation.