Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x + 4$
$y = -x + 7$
plot two lines by clicking the graph.
click a line to delete it.
(graph: coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines)
answer attempt 1 out of 2
solution: input box submit answer

Explanation:

Step1: Find intersection by solving equations

Set \(\frac{1}{2}x + 4=-x + 7\).
Add \(x\) to both sides: \(\frac{1}{2}x+x + 4=-x+x + 7\), so \(\frac{3}{2}x+4 = 7\).
Subtract 4: \(\frac{3}{2}x=7 - 4=3\).
Multiply by \(\frac{2}{3}\): \(x = 3\times\frac{2}{3}=2\).

Step2: Find y - value

Substitute \(x = 2\) into \(y=-x + 7\): \(y=-2 + 7 = 5\).

Answer:

The solution is \((2,5)\)