A system of linear equations gives two conditions that the same pair must satisfy. With decimal coefficients, graph both equations in Desmos as written and click their intersection, the point that satisfies both. Then read the coordinate the question requests. The tempting slip is to enter the second coordinate when the question asks for .
Hints
- Hint 1
A solution to a system makes both equations true. On a graph, that means it lies where the two lines cross. What point does Desmos show when you click that crossing?
- Hint 2
An ordered pair is written : comes first and comes second. Once you have the crossing point, use only the coordinate the question asks for.
Step-by-step
Approach 1: Read the Desmos intersection
Step 1Graph the first equation
Type as written. Desmos draws a line. Every point on it satisfies this equation, but one line alone doesn't determine ; the point must satisfy the second equation too.
- Step 2
Find the point and read
Add on a new line. Click where the lines cross; Desmos shows . The first coordinate of is , so the requested value is , not . Grid in 5.
Approach 2: Eliminate to find only
Step 1Make the -terms opposites
Elimination combines equations so one variable disappears. The second equation has , so multiply every term of the first equation by to turn its into :
- Step 2
Add the equations
The -terms are now opposites, so add both sides of the new equation and the second original equation:
- Step 3
Solve for
Only the requested variable remains. Divide both sides by :
So is . Grid in 5.