Question

# Solve by system of equations:5x+3y+z=-8x-3y+2z=2014x-2y+3z=20

Equations

Solve by system of equations:
$$5x+3y+z=-8$$
$$x-3y+2z=20$$
$$14x-2y+3z=20$$

2021-05-29

Step 1
Given system of equations are
$$5x+3y+z=-8$$...(1)
$$x-3y+2z=20$$...(2)
$$14x-2y+3z=20$$...(3)
Step 2
By subtracting 5 times equation (2) from equation (1), we get
$$5x+3y+z-5(x-3y+2z)=-8-100$$
$$18y-9z=-108$$
$$2y-y=-12$$...(4)
Step 3
By subtracting 14 times equation (2) from equation (3), we get
$$14x-2y+3z-14(x-3+2z)=20-280$$
$$40y-25z=-260$$
$$8y-5z=-52$$...(5)
Step 4
By subtracting 4 times equation (4) from equation (5), we get
$$8y-5z-4(2y-z)=-52+48$$
$$-z=-4$$
$$z=4$$
Step 5
By substituting $$z=4$$ in equation (4), we get value of y and then substituting values of y and z in equation (2), we get value of x
$$2y-z=-12$$
$$2y-4=-12$$
$$2y=-8$$
$$y=-4$$
$$x-3y+2z=20$$
$$x-3(-4)+2(4)=20$$
$$x+12+8=20$$
$$x=0$$
Step 6
Answer: Solution is $$x=0$$,$$y=-4$$ and $$z=4$$