Solve the system of equations.
The solution to the system is . What is the value of ?
A linear system has two equations in the same and ; its solution is where their lines cross. Graph both equations as written in Desmos and click the intersection to find the ordered pair. Then put those coordinates into the expression the question asks for. Don't stop at a number from either original equation: it may not be the requested value.
Hints
- Hint 1
Each equation traces a line. An intersection is a point on both lines, so its coordinates satisfy both equations. What point do you see when you graph the equations as written?
- Hint 2
In an ordered pair , the first coordinate is and the second is . Put each one in its matching place in ; the point itself isn't the requested value.
Step-by-step
Approach 1: Find the intersection in Desmos
Step 1Find the pair that satisfies both equations
Type and on separate Desmos lines. Click their intersection, the point on both lines. Desmos shows , so and .
- Step 2
Evaluate what the question asks for
The point isn't the answer. Substitute its first coordinate for and its second for : type . Desmos prints , so the value of is . Choice D.
Approach 2: Build the requested expression directly
Step 1Add the equations
No Desmos needed. Adding the equations builds the expression asked for. The coefficients in the requested expression are the sums of the matching coefficients in the two equations. When the left sides add to your target, add the whole equations, including their right sides. Add them here: .
- Step 2
Group matching terms
Group like terms: the -terms together and the -terms together. Keep the right side as it is: .
- Step 3
Read the value without finding either coordinate
Add the coefficients and the numbers on the right side: . So the requested expression is ; this direct combination never needed or separately. Choice D.