Linear Systems of Equations — Test

Question 10 • Mathematics 8

Consider the system of linear equations 2 x plus 3 y is equal to 8 and 3 x plus y is equal to negative 2 Which statement is correct?

Answer

The point open paren 1 comma 2 close paren is a solution to the system of equations because it satisfies the equation 2 x plus 3 y is equal to 8 .

The point open paren 1 comma 2 close paren is not a solution to the system of equations because it satisfies neither equation.

The point open paren 1 comma 2 close paren is a solution to the system of equations because it satisfies both equations.

The point open paren 1 comma 2 close paren is not a solution to the system of equations because it does not satisfy the equation 3 x plus y is equal to negative 2 .

Explanation

Substitute x = 1 and y = 2 into both equations. The first gives 2(1) + 3(2) = 8, but the second gives 3(1) + 2 = 5, not −2. Since a solution to a system must satisfy both equations, the point is not a solution; choice D is correct.

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