Which ordered pair satisfies the system of equations below?

Solution available with step-by-step explanation

SAT Systems of Two Linear Equations Question 71 | Free SAT Prep | Aniko

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Question 71·Medium·Systems of Two Linear Equations in Two Variables

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Which ordered pair $(x, y)$ satisfies the system of equations below?

2x + 3y = 12 \\[0.7em] x - y = 1

For systems of two linear equations, look for the equation that is easiest to solve for one variable (for example, $x - y = 1$ is easy to rewrite as $x = y + 1$ ). Use substitution or elimination to reduce the system to a single equation in one variable, solve it carefully, then plug back to find the other variable. On multiple-choice questions, you can also quickly test each answer by substituting the $x$ and $y$ values into both equations and seeing which pair satisfies both, but algebraic solving is usually fastest and avoids checking all four options.

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Pick the easier equation first

Between the two equations, $x - y = 1$ is simpler. Try solving that equation for $x$ or for $y$ first.

Express one variable in terms of the other

From $x - y = 1$ , isolate $x$ by adding $y$ to both sides. Then you will have an expression you can plug into the other equation.

Substitute and solve

After you write $x$ in terms of $y$ , substitute that expression into $2x + 3y = 12$ and solve the resulting equation for $y$ , then use that value to find $x$ .

Desmos Guide

Enter the first equation

In Desmos, type 2x + 3y = 12 into the first expression line. Desmos will graph this as a straight line.

Enter the second equation

In the next expression line, type x - y = 1. This will add a second line to the graph.

Find the intersection point

Look for the point where the two lines intersect. Tap or click on the intersection; Desmos will display its coordinates $(x, y)$ . Those coordinates are the solution to the system and should match one of the answer choices.

Step-by-step Explanation

Solve the simpler equation for one variable

Look at the simpler equation:

x - y = 1

Solve it for $x$ in terms of $y$ :

x = y + 1

Now you have an expression for $x$ that you can plug into the other equation.

Substitute into the first equation and solve for y

Take $x = y + 1$ and substitute it into the first equation $2x + 3y = 12$ :

2(y + 1) + 3y = 12

Distribute and combine like terms:

2y + 2 + 3y = 12

5y + 2 = 12

Subtract 2 from both sides:

5y = 10

Divide both sides by 5:

y = 2

Find x and match the ordered pair to a choice

Use $x = y + 1$ with $y = 2$ :

x = 2 + 1 = 3

So the solution to the system is the ordered pair $(x, y) = (3, 2)$ . Among the answer choices, this corresponds to choice D.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation