Solving Simultaneous Equations Using Substitution Practice

Question

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Question
Use the substitution method to solve the system 9x−3y=12
, y+6=2x
.(1 point)
(
)
Remaining Attempts : 3
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Answer 1

To solve the system of equations using the substitution method, follow these steps:

We have:

1. $9x-3y=12$ (Equation 1)
2. $y+6=2x$ (Equation 2)

Step 1: Solve one equation for one variable

Let's solve Equation 2 for $y$: $$y+6=2x$$ Subtract 6 from both sides: $$y=2x-6$$

Step 2: Substitute into the other equation

Now, substitute $y=2x-6$ into Equation 1: $$9x-3(2x-6)=12$$

Step 3: Simplify and solve for $x$

Distributing $-3$: $$9x-6x+18=12$$ Combine like terms: $$3x+18=12$$ Subtract 18 from both sides: $$3x=12-18$$ $$3x=-6$$ Divide by 3: $$x=-2$$

Step 4: Substitute back to find $y$

Now substitute $x=-2$ back into the equation we derived for $y$: $$y=2(-2)-6$$ $$y=-4-6$$ $$y=-10$$

Final Solution

The solution to the system of equations is: $$(x,y)=(-2,-10)$$

You can check both equations to ensure that these values satisfy them.