In solving a system by substitution, after expressing one variable in terms of the other, what do you do next?

In solving a system by substitution, after expressing one variable in terms of the other, what do you do next?

• A. Substitute into the other equation
• B. Solve for the other variable by substitution into a quadratic
• C. Multiply both sides
• D. Graph both equations

Answer: (A)

In solving a system by substitution, the goal is to end up with a single equation in one variable. After you express one variable in terms of the other, you replace that variable in the other equation with that expression. This substitution turns the whole system into an equation involving only one variable, which you can solve. Then you plug that value back into the expression for the first variable to get its value as well. For example, if you have x = 2y + 1 and the second equation x + y = 7, substitute x = 2y + 1 into the second equation to get (2y + 1) + y = 7, which simplifies to 3y + 1 = 7, so y = 2, and then x = 5. This shows how substitution into the other equation yields a solvable equation in one variable.

In solving a system by substitution, the goal is to end up with a single equation in one variable. After you express one variable in terms of the other, you replace that variable in the other equation with that expression. This substitution turns the whole system into an equation involving only one variable, which you can solve. Then you plug that value back into the expression for the first variable to get its value as well.

For example, if you have x = 2y + 1 and the second equation x + y = 7, substitute x = 2y + 1 into the second equation to get (2y + 1) + y = 7, which simplifies to 3y + 1 = 7, so y = 2, and then x = 5. This shows how substitution into the other equation yields a solvable equation in one variable.