Question 245·Medium·Math

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5(4y + 2) - 3(2y - 4) = 8y + 26

If $y$ is the solution to the equation above, what is the value of $9y + 1$ ?

A linear equation has a variable only to the first power, and its solution makes both sides equal. Parentheses with an outside minus sign make a Desmos regression useful: enter the whole equation without distributing. Then use the value Desmos finds in the expression the question asks for. Solving for the variable isn't the finish line when the question asks for an expression.

Hints

Hint 1
A regression asks Desmos to find a value that makes two sides equal. Desmos uses $y$ for graphing, so replace every $y$ with $t$ and enter the equation using $\sim$ instead of $=$ .
Hint 2
The value under PARAMETERS may be a rounded decimal. Type the parameter Desmos found on a new line and use its fraction button to see the exact value.
Hint 3
Finding $y$ is only the first job. The question asks for the whole expression $9y+1$ , so include both the multiplication and the addition when you evaluate it.

Step-by-step

Solve in Desmos, then evaluate
Step 1
Find the value of y
Type $5(4t+2)-3(2t-4)\sim8t+26$ . Here $t$ replaces every $y$ because Desmos uses $y$ for its graph, and $\sim$ tells Desmos to find a value that makes the sides equal. Under PARAMETERS, it shows $t\approx0.666667$ . Keep the minus before the second parentheses when you type: it applies to the whole group.
Step 2
Read the exact solution
Type $t$ on the next line and tap its fraction button. Desmos shows $\frac{2}{3}$ , so the exact solution is $y=\frac{2}{3}$ ; the value under PARAMETERS was rounded.
Step 3
Evaluate what the question asks for
Type $9t+1$ below those lines. Desmos prints $7$ , so the requested value of $9y+1$ is $7$ , not $y$ alone. Choice C.

Question 245·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this