Page 400 - Algebra 1

b. Solve the system of equations by substitution. Check your answer. 4x + 7y = 43
2x - 3y = -11 SOLUTION
Again, one equation will need to be rearranged so that it can be used for substitution. None of the variables have a coefficient of 1, so solve the second equation for x.
2x - 3y = -11
2x = 3y - 11
Write the second equation. Add 3y to both sides.
Divide both sides by 2.
Now substitute _3y - _11 for the x in the first equation. 22
4x + 7y = 43 Write the first equation. __ __
__ x = 3y - 11
22
Math Reasoning
Write When substituting the value of one variable to find the value of the other, only one equation needs to be used. So, why must both equations be used to check the answer?
4(3y-11)+7y=43 Substitute 3 y - 11 for x. 22 22
_12y-_44+7y=43 22
6y-22+7y=43 13y-22=43 13y=65
Distribute.
Simplify.
Combine like terms. Add 22 to both sides. Divide both sides by 13.
y=5
The value of y in the solution is 5. Substitute 5 into either of the original
equations to find x. First Equation
4x + 7y = 43 4x + 7(5) = 43 4x + 35 = 43
Second Equation
2x - 3y = -11 2x - 3(5) = -11 2x - 15 = -11
2x = 4 x=2 x=2
4x = 8
The solution to the system is (2, 5).
Check To determine whether the ordered pair satisfies both of the original equations, substitute the x-value and the y-value into the original equation.
First Equation
4x + 7y = 43 4(2) + 7(5) 43 8 + 35 43
43 = 43 ✓
Second Equation
2x - 3y = -11 2(2) - 3(5) -11 4 - 15 -11
-11 = -11 ✓
Lesson 59 385