A system of linear equations is a pair of equations about the same unknowns. Graph both equations in Desmos and click their intersection, the point that satisfies both. In , the first coordinate is . Check which coordinate the question asks for before you submit. If one variable has opposite coefficients, adding the equations can also give you a quick hand solution.
Hints
- Hint 1
A solution to a system makes both equations true. On a graph, that's the point where the two lines meet. Look for the intersection of both lines, not a point on only one.
- Hint 2
Desmos graphs equations with and as written. Put each equation on its own line; you don't need to rearrange either one to get alone.
- Hint 3
An ordered pair lists first and second. After you click the intersection, use the first number because the question asks for .
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph the first equation
Type into Desmos as written. Desmos draws a line; every point on it makes this equation true.
- Step 2
Graph the second equation
Type on the next line. Desmos draws a second line that crosses the first. Their crossing is a solution because it lies on both lines.
- Step 3
Read the requested coordinate
Click the intersection. Desmos labels it . In the ordered pair , the first number is , so the value of is , not or the whole pair. Grid in 3.
Approach 2: Cancel the y-terms by hand
Step 1Add the equations
The and are opposites, so they cancel when you add the equations. This is elimination: adding equal amounts on each side keeps the equation true:
Combine like terms:
- Step 2
Divide to find x
You need only , not . Divide both sides by :
Simplify: . So the value of is . Grid in 3.