The system of equations is What is one possible value of ?

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SAT Nonlinear Equations & Systems Question 178 | Free SAT Prep | Aniko

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Question 178·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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The system of equations is

\begin{aligned} x^2 + y &= 7 \\ y &= 3 \end{aligned}

What is one possible value of $x$ ?

For systems where one equation directly gives a variable (like $y=3$ ), immediately substitute that value into the other equation to reduce the system to a single equation in one variable. Then solve step by step, being careful with operations (such as subtracting instead of adding) and remembering that equations like $x^2 = k$ have two solutions, $x = \pm\sqrt{k}$ ; finally, provide any one value that satisfies the original system if the question asks for a single possible solution.

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Start with the easier equation

Look at the second equation. It already tells you the value of $y$ . How can you use that in the first equation?

Substitute into the first equation

Replace $y$ in $x^2 + y = 7$ with the value you know from the second equation, and then simplify.

Solve the resulting equation

After substituting, you will get an equation involving only $x^2$ . Isolate $x^2$ , then think about what numbers squared give that result.

Desmos Guide

Rewrite the first equation for graphing

Rewrite $x^2 + y = 7$ as $y = 7 - x^2$ so it is in the form $y = \text{(expression in } x\text{)}$ .

Enter the equations in Desmos

In one line, type y = 7 - x^2. In another line, type y = 3. You will see a downward-opening parabola and a horizontal line.

Find the intersection points

Click on the intersection points of the parabola and the line. Note the $x$ -coordinates of these intersection points; either of those $x$ -values is a valid solution to the system.

Step-by-step Explanation

Use the given value of y

From the second equation, you know that $y=3$ .

Substitute $3$ for $y$ in the first equation $x^2 + y = 7$ .

Form and simplify the equation in x

After substituting $y=3$ , the first equation becomes

x^2 + 3 = 7

Subtract $3$ from both sides to isolate $x^2$ :

x^2 = 4

Solve for x and answer the question

To solve $x^2 = 4$ , take the square root of both sides:

x = 2 \text{ or } x = -2

Both values satisfy the system, but the question asks for one possible value of $x$ , so you can give $2$ as your answer.

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Step-by-step Explanation

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Step-by-step Explanation