Solve this simultaneous equation using graphical method: y=x+4, y+x=10, y=x+2, y=2x−14.

Question

ScanSolve AI Tutor · Accepted Answer

To solve a system of simultaneous equations using the graphical method, we plot each equation as a line on a coordinate plane. The point where the lines intersect is the solution to the system.

Given the list of expressions, we will solve the first two distinct linear equations:

$y = x + 4$
$y + x = 10 \implies y = -x + 10$

Find two points for each equation to plot the lines.
For the first equation, $y = x + 4$ :
- If $x = 0$ , $y = 0 + 4 = 4$ . Point: $(0, 4)$
- If $x = 2$ , $y = 2 + 4 = 6$ . Point: $(2, 6)$
For the second equation, $y = -x + 10$ :
- If $x = 0$ , $y = -0 + 10 = 10$ . Point: $(0, 10)$
- If $x = 5$ , $y = -5 + 10 = 5$ . Point: $(5, 5)$
Plot these points on a graph and draw a straight line through the points for each equation.
(Imagine a graph where these lines are drawn.)
Identify the point of intersection.
When you plot these lines, you will observe that they intersect at a single point. To find this point algebraically (which you would verify graphically):
Set the expressions for $y$ equal to each other:
$x + 4 = -x + 10$
Add $x$ to both sides:
$2x + 4 = 10$
Subtract 4 from both sides:
$2x = 6$
Divide by 2:
$x = 3$
Substitute $x = 3$ into either equation (e.g., $y = x + 4$ ):
$y = 3 + 4$ $y = 7$
The lines intersect at the point $(3, 7)$ .
State the solution.
The solution to the system of simultaneous equations is the point of intersection.

Solve this simultaneous equation using graphical method: y=x+4, y+x=10, y=x+2, y=2x−14.

Answer

Step-by-step solution

Find two points for each equation to plot the lines.

Plot these points on a graph and draw a straight line through the points for each equation.

Identify the point of intersection.

State the solution.

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