Question 271·Easy·Algebra

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If $5y - 7 = 18$ , what is the value of $10y + 3$ ?

Your answer

A linear equation has its unknown to the first power, but the question may ask for an expression built from that unknown instead. Use a Desmos regression to find the unknown, then enter the entire requested expression. Stopping at the value of the unknown solves the equation but leaves the question unanswered.

Hints

Hint 1
A regression asks Desmos to find a value that makes an equation true. Use $y_1$ in place of the problem’s $y$ , and replace the equals sign with $\sim$ . What value does Desmos report?
Hint 2
The solution to the equation is not automatically the answer. Put that value into $10y+3$ , then evaluate the whole expression.

Step-by-step

Approach 1: Solve and evaluate in Desmos
Step 1
Find the value of $y$
Type $5y_1-7\sim18$ . Desmos uses $y$ for its graph, so $y_1$ stands for the problem’s $y$ . The regression symbol $\sim$ tells Desmos to find the value that makes both sides equal. Under PARAMETERS, it reports $y_1=5$ .
Step 2
Evaluate what the question asks for
Type $10y_1+3$ on the next line. Desmos uses $y_1=5$ and prints $53$ . That’s the value of $10y+3$ , not just $y$ . Grid in 53.

Approach 2: Use the whole side of the equation
Step 1
Double the equation’s left side
The target starts with $10y$ , which is twice $5y$ . Double the whole left side, including its $-7$ :
$2(5y-7)=10y-14.$
Step 2
Adjust to match the target
The target ends in $+3$ , which is $17$ more than $-14$ . Add $17$ to make the expressions match:
$10y+3=2(5y-7)+17.$
Step 3
Replace the known expression
The given equation says $5y-7=18$ , so replace that whole expression with $18$ :
$10y+3=2(18)+17.$
Step 4
Calculate the requested value
Type $2(18)+17$ into Desmos. It prints $53$ , the value of $10y+3$ . Grid in 53.

Question 271·Easy·Algebra

Strategy

Hints

Step-by-step

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Strategy

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Step-by-step

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