We will use the Substitution Method to solve this system of equations. It is usually the best choice when one of the variables is already isolated or has a coefficient of 1 or -1. In the second equation, y is already solved for, so we can substitute it in the first equation to find x.
Solving this system of equations resulted in an identity; 10 is always equal to itself. Therefore, the lines are the same and have infinitely many intersection points.
b
We will use the Elimination Method to solve this system of equations. It is usually the best choice when one of the variables has equal or opposite coefficients, as they are in the given equation.
We can check our solution by substituting x= 13 and y=- 32 into the original system of equations. If the left-hand side and right-hand side are equal in both equations, the solution is correct.
Both equations are true, so our solution is correct!
c
To solve this system of equations we will again use the Substitution Method. In the second equation, y is already solved for, so we can substitute it in the first equation to find x.
We can check our solution by substituting x=1 and y=2 into the original system of equations. If the left-hand side and right-hand side are equal in both equations, the solution is correct.
Both equations are true, so our solution is correct!
d
We will use the Equal Values Method to solve this system of equations. It is a good choice when both of the equations are in y=mx+b form. Having two expressions that equal y, we will start by setting them equal to each other.
y= 14x+5 y= 2x-9 ⇒ 14x+5= 2x-9
Now let's solve this equation for x.
We can check our solution by substituting x=8 and y=7 into the original system of equations. If the left-hand side and right-hand side are equal in both equations, the solution is correct.
y= 14x+5 & (I) y=2x-9 & (II)
(I), (II): x= 8, y= 7
7? = 14( 8)+5 7? =2( 8)-9
(I), (II): Multiply
7? =2+5 7? =16-9
(I), (II): Add and subtract terms
7=7 7=7
Both equations are true, so our solution is correct!
