A system of linear equations gives two rules for the same and . Type both equations as written in Desmos, then click where their lines cross: that point satisfies both rules. An ordered pair lists first, so don't enter the first coordinate when the question asks for . Match the requested variable to its coordinate.
Hints
- Hint 1
An intersection is a point on both lines, so its coordinates make both equations true. Desmos can graph the equations as written; you don't need to rearrange either one. Where do the lines meet?
- Hint 2
An ordered pair lists coordinates as : first , then . Click the crossing point rather than estimating from the grid. The second coordinate gives the variable this question asks for.
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Connect the solution to a shared point
The pair must satisfy both equations. On a graph, that means it lies at their intersection, the point where the two lines cross. So you can graph the equations without solving either one for .
- Step 2
Click the point and read the requested coordinate
Type and on separate Desmos lines. Click where they cross; Desmos shows . In , is the second coordinate, so the requested value is . Grid in 3.
Approach 2: Eliminate x by subtracting equations
Step 1Match the x terms
Multiply every term of by so its term matches the first equation's :
- Step 2
Subtract to remove x
Subtract the whole new equation from to make the terms cancel:
- Step 3
Distribute the minus sign
The minus sign changes both terms inside the second parentheses:
- Step 4
Combine the remaining terms
Combine like terms. The terms cancel, leaving an equation in alone:
- Step 5
Find y
Divide both sides by :
So the value of is . Grid in 3.