Answer:
true
Explanation:
substitution method
A method used to solve systems of equations by solving an equation for one variable and substituting the resulting expression into the other equation(s).
y = 2x
y = x + 5
Step 1
y = 2x
y = x + 5
Step 2
plug 2x into y = x + 5 for y
2x = x + 5
Step 3
solve for x
2x − x = x − x + 5
x = 5
Step 4
plug x = 5 into y = 2x
y = 2(5)
y = 10
Step 5
solution
(5, 10)
USE WHEN...
• A variable in either equation has a coefficient of 1 or −1.
• Both equations are solved for the same variable.
• Either equation is solved for a variable.
EXAMPLE
x + 2y = 7
x = 10 − 5y
or
x = 2y + 10
x = 3y + 5
elimination method
A method used to solve systems of equations in which one variable is eliminated by adding or subtracting two equations of the system.
x − 2y = −19
5x + 2y = 1
Step 1
x − 2y =−19
+5x + 2y = 1
∴ 6x + 0 =>−18
Step 2
6x = −18
6x ÷ 6 = −18 ÷ 6
x = −3
Step 3
plug x = -3 into x − 2y = −19
now, solve −3 − 2y = −19 for y
−3+ 3 − 2y = −19 + 3
−2y = −16
y = 8
Step 4
solution
(−3,8)
USE WHEN...
• Both equations have the same variable with the same or opposite coefficients.
• A variable term in one equation is a multiple of the corresponding variable term in the other equation.
EXAMPLE
3x + 2y = 8
5x + 2y = 12
or
6x + 5y = 10
3x + 2y = 15