An intersection must satisfy both equations

Graph an equation's two sides

For $3x+7=22$, enter $y=3x+7$ and $y=22$. At their intersection, the outputs match. Its $x$-coordinate, $5$, solves the original equation. You can also enter the one-variable equation directly in SAT Desmos; the two-graph method makes the equal outputs visible.

An intersection readout may be rounded. Substitute a candidate into the original equation, especially when a denominator, square root, or restricted domain is involved.

Standard-form systems can go straight into SAT Desmos

SAT Desmos accepts $3x+2y=13$ and $5x-y=13$ directly. Their intersection is $(3,2)$. Our guided example rewrites them as $y=(13-3x)/2$ and $y=5x-13$ to show how each line works.

If the question asks for $2x-y$, finish with $2(3)-2=4$. If it asks only for $y$, report $2$. Keep the requested quantity in view before selecting an answer.

$\displaystyle y=\frac{13-3x}{2}$

Divide the entire difference by 2.

$\displaystyle y=5x-13$

The same second equation with y isolated.

A graph window alone cannot prove how many solutions exist

Distinct parallel lines have no intersection: $y=2x+1$ and $y=2x+4$ have equal slopes and different intercepts. The equations $y=2x+1$ and $2y=4x+2$ describe the same line, so infinitely many pairs satisfy both.

Two lines that merely look parallel or overlapping at one zoom level do not establish either conclusion. Compare the coefficients. For nonlinear graphs, inspect the relevant domain and check whether additional crossings lie outside the current window.

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