Do the equations have to be solved for y before graphing them?

No. An equation such as 3x + 7y = 122 can be typed as it is printed and the calculator draws the same line. Rearranging first only adds a place to slip.

What if the lines do not cross on the screen?

Zoom out or drag the graph. Totals in the hundreds put the crossing point well outside the starting window. If the lines still never meet, they may be parallel, and that is a question to settle with the coefficients, not by eye.

Is graphing faster than substitution or elimination?

When the two equations are in different forms or come from a word problem, usually. When they are already lined up so that adding them removes a variable, elimination is faster than typing.

The crossing point has decimal coordinates and the choices are fractions. What then?

Turn the choices into decimals and compare. A crossing at 1.625 is the choice that says 13 over 8.

Solve a system of equations by graphing both lines

Type both equations as they are printed. The point where the two graphs cross is the one pair $(x, y)$ that satisfies both.

1.Type each equation on its own row, in whatever form it is printed. There is no need to solve for $y$ first.
2.Tap either line. The crossing point is marked with its coordinates.
3.Read the question again. It may want $x$ , $y$ , or something built from both, such as $x + y$ .

Try it on a question

Work it below before you open the working. The steps say what to do, and you can do each one yourself.

A stall sells small candles for $3 each and large candles for $7 each. One day it sold 26 candles for a total of $122. How many large candles did it sell that day?

Choice A: $11$
Choice B: $13$
Choice C: $15$
Choice D: $17$

1
Let $x$ be the small candles and $y$ the large ones. The first sentence counts candles: 26 in all.
Type: x + y = 26
2
The second sentence totals the money: $3 for each small candle, $7 for each large one, $122 in all.
Type: 3x + 7y = 122
3
Find the answer on the graph. Tap a line or a curve to mark its points.

Open in the full calculator

Loading the calculator…

The full working, and why each wrong choice is there

Let $x$ be the number of small candles and $y$ the number of large ones. The count gives $x + y = 26$ . The money gives $3x + 7y = 122$ .

By hand: $x = 26 - y$ , so $3(26 - y) + 7y = 122$ , which is $78 + 4y = 122$ and $y = 11$ .

In the calculator: type both equations and tap a line. They cross at $(15, 11)$ : 15 small and 11 large. The question asks for the large candles, so the answer is 11.

Choice A: $11$ the answer
With $x$ small and $y$ large candles, $x + y = 26$ and $3x + 7y = 122$ . The lines cross at $(15, 11)$ , and $y$ is the large candles.
Choice B: $13$
This is half of 26, which assumes the stall sold the same number of each. Nothing in the question says so.
Choice C: $15$
This is the number of small candles. The question asks for the large ones.
Choice D: $17$
This is $122 divided by $7 and rounded down, as if every candle sold were large.

Use it when

Two linear equations, and the question asks for $x$ , $y$ or a combination of the two.
The equations are printed in different forms, so substitution or elimination would need rearranging first.
A word problem whose two sentences become two equations: one that counts things and one that totals them.

Do not use it when

The question asks how many solutions the system has, or for the constant that gives none. Compare the ratios of the coefficients: two lines that look parallel on a screen may not be.
The system is already lined up, such as $x + y = 10$ and $x - y = 4$ . Adding the two equations takes five seconds.
A coefficient is a letter. The calculator needs a number for it before it can draw anything.

Five questions on this move

Untimed, and nothing is saved. A wrong first answer gets one more try before the working is shown.

Question 1 of 5

$2x + 3y = 12$
$y = x - 1$

The solution to the given system of equations is $(x, y)$ . What is the value of $x$ ?

Five is a start

In your account there is a focused set of ten on Systems of two linear equations in two variables from the question bank, with the same one more try. And after each practice test, the drills your plan sets for the skills you missed name the moves for them.

Practise Systems of two linear equations in two variables in your account

How this page was checked

Every maths answer, by our own calculator
The answer to each of the 6 questions on this page is worked out again by our calculator engine in an automated test, which fails when a key disagrees with the engine.
In the calculator the test uses
Claude (an AI assistant) typed this page's calculator steps into the College Board version of the Desmos calculator on 14 October 2026 and read the same answers. All six systems on this page were typed in exactly as printed, and each crossing was the keyed point.
The whole page, by a person
Not yet. Every question and every step of its walk-through was worked through in a browser by Claude, an AI assistant, on 14 October 2026. The page was published on 14 October 2026 before a person had read it. If something here is wrong, tell us and it is put right.

The questions were drafted with AI and are original: none is a College Board question, and none comes from the question bank behind our practice tests.

Where this comes from

“Two graphs, one crossing” is one card from the Preptics lesson Systems from a word problem: one sentence counts, one totals, which sits under the Digital SAT skill Systems of two linear equations in two variables. The lesson has the other cards around it, and its questions come back for review on a schedule. The lessons are part of the Digital SAT track.

Common questions

Do the equations have to be solved for y before graphing them?: No. An equation such as 3x + 7y = 122 can be typed as it is printed and the calculator draws the same line. Rearranging first only adds a place to slip.
What if the lines do not cross on the screen?: Zoom out or drag the graph. Totals in the hundreds put the crossing point well outside the starting window. If the lines still never meet, they may be parallel, and that is a question to settle with the coefficients, not by eye.
Is graphing faster than substitution or elimination?: When the two equations are in different forms or come from a word problem, usually. When they are already lined up so that adding them removes a variable, elimination is faster than typing.
The crossing point has decimal coordinates and the choices are fractions. What then?: Turn the choices into decimals and compare. A crossing at 1.625 is the choice that says 13 over 8.

Keep going

Every move: the full set. The calculator on its own: the graphing calculator.

SAT® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this site. All practice questions and reading passages are original works created by Preptics and are not actual SAT® questions.