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$31 x−4=-2x+10$

MultEqn$LHS⋅3=RHS⋅3$

$(31 x−4)⋅3=(-2x+10)⋅3$

DistrDistribute $3$

$x−12=-6x+30$

AddEqn$LHS+6x=RHS+6x$

$7x−12=30$

AddEqn$LHS+12=RHS+12$

$7x=42$

DivEqn$LHS/7=RHS/7$

$x=6$

b

Let's solve the system of equations by graphing. Thus, we must identify each line's key features.

Feature | $y=31 x−4$ | $y=-2x+10$ |
---|---|---|

Slope | $31 $ | $-2$ |

$y$-intercept | $-4$ | $10$ |

Now, we can graph the equations.

We can see that the graphs intersect at the point $(6,-2).$ This is the solution of the system of the equations.

c

The equation in part A is $31 x−4=-2x+10.$ The system of equations from part B is ${y=31 x−4y=-2x+10. $ The first function in the system corresponds to the left-hand side in the equation.

d

$Part A:Part B: x=6(6,-2) $ As discussed in part C, the left- and right-hand side of the equation in part A represented the functions in part B. Therefore, the $x$-value is the same in the two answers. $Part A:Part B: x=6(6,-2) $ However, in part B we got a value of $y$ as well. This is because the equations are separated in part B but not in part A.