The solution to a system of equations can be found graphically by graphing each equation. The solution is the point of intersection of the equations. Find the solution to the system
Below:
$$\begin{array} { l }
y = \frac { 3 } { 4 } x + 2 \
y = - \frac { 1 } { 2 } x + 7
\end{array}$$
A)(5, 4)
B)(3, 5)
C)(4, 6)
D)(4, 5)

Question

The solution to a system of equations can be found graphically by graphing each equation. The solution is the point of intersection of the equations. Find the solution to the system
Below:
$$\begin{array} { l } 
y = \frac { 3 } { 4 } x + 2 \
y = - \frac { 1 } { 2 } x + 7
\end{array}$$
A)(5, 4)
B)(3, 5)
C)(4, 6)
D)(4, 5)

Quizplus · Accepted Answer

To solve the system of equations, we can graph each equation and find the point at which they intersect.

Plotting the first equation, y = (3/4)x + 2, we can start at the y-intercept of 2 and use the slope of 3/4 to find additional points on the line. For example, if we move right one unit (i.e. x = 1), we move up 3/4 units (i.e. y = 2.75). Plotting a few more points and connecting them gives us the line:

y = (3/4)x + 2

Plotting the second equation, y = (-1/2)x + 7, we can start at the y-intercept of 7 and use the slope of -1/2 to find additional points on the line. For example, if we move right two units (i.e. x = 2), we move down one unit (i.e. y = 6). Plotting a few more points and connecting them gives us the line:

y = (-1/2)x + 7

At this point, we can see that the lines intersect at a point that appears to be (4, 5). To check, we can substitute x=4 and y=5 into each of the equations:

y = (3/4)x + 2
5 = (3/4)(4) + 2
5 = 3 + 2
5 = 5

and

y = (-1/2)x + 7
5 = (-1/2)(4) + 7
5 = -2 + 7
5 = 5

Both equations are true when x=4 and y=5, so this is indeed the solution to the system. Therefore, the answer is D) (4, 5).

The Solution to a System of Equations Can Be Found y=34x+2y=−12x+7\begin{array} { l } y = \frac { 3 } { 4 } x + 2 \\y = - \frac { 1 } { 2 } x + 7\end{array}y=43​x+2y=−21​x+7​

The Solution to a System of Equations Can Be Found $\begin{array} { l } y = \frac { 3 } { 4 } x + 2 \\y = - \frac { 1 } { 2 } x + 7\end{array}$