Solve each equation for y. See Sections 2.5 and 3.3.Solve each equation. Check the solution. See Section 2.3.
- 4 x- 211 - 3 x 2 = 6 60.t+ 312 t- 42 =- 13
- 21 x- 22 + 5 x= 10 4 13 - 2 k 2 + 3 k= 12
3 x+y= 4 - 2 x+y= 9 9 x- 2 y= 4 5 x- 3 y= 12PREVIEW EXERCISES
SECTION 4.2 Solving Systems of Linear Equations by Substitution 257
OBJECTIVES
Solving Systems of Linear Equations by Substitution
4.2
1 Solve linear systems
by substitution.
2 Solve special
systems by
substitution.
3 Solve linear systems
with fractions and
decimals by
substitution.
OBJECTIVE 1 Solve linear systems by
substitution. Graphing to solve a system of
equations has a serious drawback. For example,
consider the system graphed in FIGURE 7. It is
difficult to determine an accurate solution of
the system from the graph.
As a result, there are algebraic methods for
solving systems of equations. The substitution
method,which gets its name from the fact that
an expression in one variable is substitutedfor
the other variable, is one such method.
xy032 x + 3y = 65x – 3y = 5
25- 3
FIGURE 7Using the Substitution MethodSolve the system by the substitution method.
(1)y= 2 x (2)
3 x+ 5 y= 26
EXAMPLE 1
Equation (2), is already solved for so we substitute 2xfor yin
equation (1).
(1)
Let.
Multiply.
Combine like terms.x= 2 Divide by 13.
13 x= 26
3 x+ 10 x= 26
3 x+ 512 x 2 = 26 y= 2 x
3 x+ 5 y= 26
y= 2 x, y,
We number the equations
for reference in our discussion.Don’t stop here.Now we can find the value of yby substituting 2 for xin either equation. We choose
equation (2).
(2)
Let.y= 4 Multiply.
y= 2122 x= 2
y= 2 x
The exact coordinates of
the point of intersection
cannot be found from
the graph.