Question

Solve the system of linear equations using multiplication.

Answer 1

Answer:

$(8,-1)$

Step-by-step explanation:

The given system is:

$3x+3y=21$

$6x+12y=36$

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

$x+y=7$

$x+2y=6$

We could solve the first equation for $x$ and replace the second $x$ with that.

Let's do that.

$x+y=7$

Subtract $y$ on both sides:

$x=7-y$

So we are replacing the second $x$ in the second equation with $(7-y)$ which gives us:

$(7-y)+2y=6$

$7-y+2y=6$

$7+y=6$

$y=6-7$

$y=-1$

Now recall the first equation we arranged so that $x$ was the subject. I'm referring to $x=7-y$.

We can now find $x$ given that $y=-1$ using the equation $x=7-y$.

Let's do that.

$x=7-y$ with $y=-1$:

$x=7-(-1)$

$x=7+1$

$x=8$

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

$3x+3y=21$ with $(x,y)=(8,-1)$:

$3(8)+3(-1)=21$

$24+(-3)=21$

$21=21$ is a true equation so the "solution" looks promising still.

$6x+12y=36$ with $(x,y)=(8,-1)$:

$6(8)+12(-1)=36$

$48+(-12)=36$

$36=36$ is also true so the solution has been verified since both equations render true for that point.

Answer 2

3x + 3y = 21

6x + 12y = 36

$\frac{6x + 12y=36}{6} \\\\x+2y=6\\\\x=6-2y\\----------\\3(6-2y)+3y=21\\\\18-6y+3y=21\\\\18-3y=21\\\\-1(-3y=3)\\\\3y=-3\\\\y=-1$

$3x+3y=21\\\\3x+3(-1)=21\\3x-3=21\\3x=24\\x=8$

x = 8 and y = -1

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