a Use the Substitution Method and then use slope and y-intercept to graph the equations.
B
b Use the Substitution Method and then use slope and y-intercept to graph the equations.
A
a (1,1)
B
b (-1,3)
Practice makes perfect
a Let's start with solving the system algebraically. We will use the Substitution Method to solve this system of equations. It is usually the best choice when one of the variables is already isolated or has a coefficient of 1 or -1. In the first equation, y is already solved for, so we can substitute it in the second equation to find x.
We can confirm our solution by graphing the equations on the same set of axes. To do this we should rewrite them into the slope-intercept form.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
y=3x-2
y=3x+( -2)
3
(0, -2)
4x+2y=6
y=-2x+ 3
-2
(0, 3)
To graph each line, we will plot the y-intercept first, then we will use the slope to find another point. Connecting the points will draw the line for each equation.
The lines intersect at (1,1), so we confirmed that our solution is correct.
b Again we will start with solving the system algebraically. Since in the first equation x is already solved for, we will use the Substitution Method to solve this system of equations.
We can confirm our solution by graphing the equations on the same set of axes. To do this we should rewrite them into the slope-intercept form.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
x=y-4
y=x+ 4
1
(0, 4)
2x-y=-5
y=2x+ 5
2
(0, 5)
To graph each line, we will plot the y-intercept first, then we will use the slope to find another point. Connecting the points will draw the line for each equation.
The lines intersect at (-1,3), so we confirmed that our solution is correct.
