The solution to the system of given equations is (6, -8). Hence, option C is the right choice.
What is the system of equations?
A system of equations is a set of equations involving more than one variable, use to find the solutions to these variables simultaneously.
How to solve the question?
In the question, we are given a system of equations,
y = 1/3x - 10 ... (i),
2x + y = 4 ... (ii).
We are asked to find the solution to this system of equation.
To solve the system of equations we substitute the value of y = 1/3x - 10 from (i) in (ii), to get:
2x + (1/3x - 10) = 4, which is a linear equation in the variable x.
Now we solve this equation to find the value of x, as follows:
2x + 1/3x - 10 = 4 {simplifying},
or, 7/3x = 14 {adding the fractions and moving 10 to the right side of the equation},
or, x = 14*3/7 {cross multiplying},
or, x = 6 {simplifying}.
Thus, we get the value of x = 6.
We substitute this value in (i), to find the value of y.
y = (1/3)6 - 10,
or, y = 2 - 10 = -8.
Thus, we get the value of y = -8.
Thus, the solution to the system of given equations is (6, -8). Hence, option C is the right choice.
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