Question 369·Medium·Algebra

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\begin{cases} y = 7 - 3x \\[4pt] 2x + y = -4 \end{cases}

The ordered pair $(x, y)$ satisfies the system of equations above. What is the value of $y$ ?

Your answer

A system of equations gives two conditions that the same pair $(x,y)$ must satisfy. Graph both equations in Desmos and click where their lines meet; that point satisfies both conditions. An ordered pair lists $x$ first and $y$ second, so if the question asks for $y$ , use the second coordinate, not the first.

Hints

Hint 1
An intersection is a point on both graphed lines. Since the pair must satisfy both equations, type each equation into Desmos as written. Where do the lines cross?
Hint 2
An ordered pair $(x,y)$ lists $x$ first and $y$ second. After you click the crossing, read the second number. The first number is part of the solution, but it isn't the value requested.

Step-by-step

Approach 1: Graph both equations
Step 1
Find where both equations hold
Type $y=7-3x$ and $2x+y=-4$ on separate Desmos lines. Desmos shows two lines crossing once. Their intersection is the point that makes both equations true, so there's no need to rearrange either equation.
Step 2
Read the requested coordinate
Click the crossing. Desmos labels the point $(11,-26)$ . In the ordered pair $(x,y)$ , $y$ comes second, so read the second coordinate when asked for $y$ . The value of $y$ is $-26$ . Grid in -26.

Approach 2: Substitute the expression for $y$
Step 1
Replace $y$ in the second equation
The first equation says $y$ equals the whole expression $7-3x$ . Use substitution, replacing $y$ in the second equation with that equal expression: $2x+(7-3x)=-4$ .
Step 2
Combine the $x$ -terms
Combine the like terms $2x$ and $-3x$ ; together they make $-x$ : $7-x=-4$ . Keep the negative sign on $x$ .
Step 3
Isolate $-x$
Subtract $7$ from each side: $-x=-11$ .
Step 4
Find $x$
Divide both sides by $-1$ : $x=11$ . That's the first coordinate; you still need the requested $y$ -value.
Step 5
Evaluate $y$
Put $x=11$ into $y=7-3x$ . Type $7-3(11)$ in Desmos; it displays $-26$ . So the requested value of $y$ is $-26$ . Grid in -26.

Question 369·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this