What could you observe in the two equations that are for substitution and elimination? And could they work on the methods as together? Yes, they can! It’s not the easiest way to do that.
The substitution is meant for the variable to be alone in the equation. Which would be easier to make the y-intercept of slope form to substitute your variable to the second equation you have used. This would help to solve your intercepts for two lines, where they could intercept in the graph to give you one point! Which would lead you to verify them, as for example, the following equations are x+4y= 17 and 2x-y=7. Which gives the point of (5,3) to the intersecting lines, where you could verify them in any of the equation, the variables would be substituted to this equation that helps to check that one side is equal to the other side. And you’re correct!
The elimination was used to get rid of the zero pair from the bases, you may multiply the coefficient to balance with your other equation. Which is going to affect your values in the equation for their signs, to switch as a negative.
These are mostly used to add from the values on the equations, and they are to combine. It sounds weird, but let me show you a visual.
These equations may eliminate, as the pair of the twos have opposite signs. This leads to seeing that you can add the y-values, and subtract the constants as they have a negative sign. You follow by their integer sign to know what you are doing. Then you would divide the variable to lead you the y-intercept.
Now, you have the intercept, you would replace to the variable of the following equation that look easier to solve. How would I know? You can see that the values are smaller, and when there are two negative, then they would become a positive! This method is used to verify as well.
What are the weapons to defeat this battle? There are three that’s the best suit for you.
The first weapon is the one solution where the equation has the slopes that are different to another, they are not matched as perfect. When meeting their enemy in their battling point – the point of the two lines that intersects. The second weapon is no solution, where the slopes are the same and the intercepts are different. It gives you a parallel line in graphing as the 3x+5y=15, where you have switched the integer of the y-variable to one side and the values goes to the left. This leads to diving the coefficient to find the intercept of y= -3/5x +3. And compare to the other equation of y=-3/5x. They have a little change to their intercept.
The final weapon to introduce is the infinity solutions, as they are many points in one line, who have the whole value for the following equation. This means the slopes and y-intercepts are the same, when you have solved the two equations that are given. It leads to a perfect line on the graph.