Question

Solve the system of equations using substitution or elimination by addition.

x + y = 0.2
-0.5x + 0.7y = -0.94

Select the correct choice below and if necessary, fill in the answer box to complete your choice.

A.The solution is ___ ​(Type an ordered​ pair.)
B.There are infinitely many solutions.
C.There is no solution.

Answer 1

A. The solution is (0.9,-0.7)

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

( 0.9 ,− 0.7 )

Equation Form:

x = 0.9 & y = − 0.7

Answer 2

Answer: A. The unique solution to the system is
`(0.9,-0.7)`

Explanation:

You can follow these steps to solve the system of equation by the Elimination Method:

- Multiply the first equation by 0.5, then add both equations and solve for "y":

`\left \{ {{0.5(x + y) = 0.5(0.2)} \atop {-0.5x + 0.7y = -0.94}} \right.\\\\\left \{ {{0.5x + 0.5y = 0.1} \atop {-0.5x + 0.7y = -0.94}} \right.\\...............................\\1.2y=-0.84\\y=-0.7`

- Substitute the value of "y" into any original equation to find the value of "x". Then:

`x + (-0.7) = 0.2\\\\x=0.2+0.7\\\\x=0.9`

Therefore, the unique solution to the system is
`(0.9,-0.7)`