Question 289·Easy·Algebra

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The system of equations is

\begin{cases} 2x + y = 9 \\ y = 3 \end{cases}

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

Your answer

A system of equations asks for numbers that make both equations true at once. If one equation fixes $y$ at a number, its graph is horizontal, and its intersection with the other line gives the solution pair. Enter both equations as written in Desmos and click where they cross. If the question wants $x$ , read the first coordinate, not the entire pair.

Hints

Hint 1
A system means the same pair $(x,y)$ must work in both equations. If one equation gives you $y$ directly, what must be true about the second coordinate of the solution?
Hint 2
An intersection is where two graphs meet, so its coordinates make both equations true. Graph the equations as written and click their meeting point. Which coordinate gives you $x$ ?

Step-by-step

Approach 1: Read the intersection in Desmos
Step 1
Identify where the solution must lie
Because $y=3$ fixes the second coordinate, it graphs as a horizontal line. In a system, the solution must lie on both graphs, so look for where that line crosses $2x+y=9$ .
Step 2
Read the requested coordinate
Type $2x+y=9$ and $y=3$ on separate lines in Desmos. Click their intersection, the point shared by both lines. Desmos shows $(3,3)$ . The first coordinate is $x$ , so $x=3$ . Grid in 3.

Approach 2: Substitute the known value
Step 1
Replace y in the other equation
Since $y=3$ , substitution means putting $3$ in place of $y$ in the other equation: $2x+3=9$
Step 2
Isolate the x-term
Subtract $3$ from both sides: $2x=6$ The $6$ is still $2x$ , not $x$ .
Step 3
Find x
Divide both sides by the coefficient $2$ , the number multiplying $x$ : $x=3$ So the requested value of $x$ is $3$ . Grid in 3.

Question 289·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

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