Solve the following system. ) x+3y=1 -2y-z=1 4x-3z=13 x= square y.= square z= square

Question

Answer 1

To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method.First, let's eliminate

from the first and third equations. Multiply the second equation by 3 to make the coefficients of

in the second and third equations equal:

Now, add the second and third equations to eliminate

:

Simplify:

Now, we have a new system of equations:

Subtract the first equation from the second equation to eliminate

:

Simplify:

Divide both sides by 4:

Now that we have the value of

, we can substitute it back into the first equation to solve for

:

Subtract

from both sides:

Simplify:

3y=-\frac{9}{4}

y=-\frac{3}{4}

x

y

z

-2(-\frac{3}{4})-z=1

\frac{3}{2}-z=1

\frac{3}{2}

-z=1-\frac{3}{2}

-z=\frac{2}{2}-\frac{3}{2}

-z=-\frac{1}{2}

z=\frac{1}{2}

x=\frac{13}{4}

y=-\frac{3}{4}

z=\frac{1}{2}$

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