Page 399 - Algebra 1

So far, every system of equations has had at least one equation of the form
y = mx + b or x = my + b. If neither equation is in this form, the first step is to rearrange one of the equations.
Rearrange Before Substitution
a. Solve the system of equations by substitution. Check your answer. 2x + y = -4
5x - 2y = -1 SOLUTION
Because neither equation is in a form that can be used for substitution, one equation will need to be rearranged. The first equation can be rearranged to be in the form y = mx + b easily because the coefficient of y is 1.
2x + y = -4 Write the first equation.
y = -2x - 4 Subtract 2x from both sides.
Now substitute -2x - 4 for y in the second equation.
5x-2y=-1 Write the second equation. 5x-2(-2x-4)=-1 Substitute -2x - 4 for y.
5x+4x+8=-1 Distribute. 9x+8=-1 Combine like terms.
9x=-9 Subtract 8 from both sides. x=-1 Divide both sides by 9.
The value of x in the solution is -1. The y-value can be found by substituting -1 into either of the original equations.
Hint
Use the variable with the coefficient of 1 whenever possible.
Example
3
Caution
Be sure to distribute the negative sign with the number.
First Equation
2x + y = -4 2(-1) + y = -4 -2 + y = -4 y = -2
Second Equation
5x - 2y = -1 5(-1) - 2y = -1 -5 - 2y = -1
-2y = 4
y = -2
The solution to the system is (-1, -2).
Check To check that this ordered pair satisfies both of the original
Hint
When neither variable has a coefficient of 1, choose a variable with a small coefficient or one that easily divides into the other coefficients and constants in the equation.
384 Saxon Algebra 1
equations, substitute
First Equation
2x + y = -4 2(-1) + (-2) -4 -2 + (-2) -4 -4=-4
the x-value and y-value into the original equations. Second Equation
✓
5x - 2y = -1 5(-1) - 2(-2) -1 -5 + 4 -1
-1=-1 ✓