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Chapter 5: Q. 5.53 (page 618)

Solve the system by elimination.

4x-3y=15x-9y=-4

Short Answer

Expert verified

The solution of the system is(x,y)=(1,1).

Step by step solution

01

Step 1.Given information

The given system is4x-3y=15x-9y=-4

02

Step 2. Solve for x

4x-3y=15x-9y=-4given-3(4x-3y=1)鈬�-12x+9y=-3Multiplyfirstequationwith-35x-9y=-4

Add both equations

-12x+9y=-35x-9y=-4-7x=-7x=-7-7Solveforxx=1

03

Step 3. Solve for y

5x-9y=-4Secondequation5(1)-9y=-4Substitutex=15-9y=-4Solvefory-9y=-4-5-9y=-9y=-9-9y=1

Hence, the solution is (x,y)=(1,1).

04

Step 4. Verify the solution

4x-3y=1鈬�4(1)-3(1)=14-3=11=1true5x-9y=-4鈬�5(1)-9(1)=-45-9=-4-4=-4true

Both equations are true.

Hence, the solution is(x,y)=(1,1).

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Most popular questions from this chapter

Solve the system of equationsx+y=10,x-y=6

(a) by graphing

(b) by substitution

(c) Which method do you prefer? Why?

Solve a System of Equations by Elimination -

3x-4y=-11x-2y=-5

Determine whether an ordered pair is a solution of a system of equations. In the following exercises, determine if the following points are solutions to the given system of equations.

x+5y=10y=35x+1

(a)(-10,4)

(b)54,74

Determine whether an ordered pair is a solution of a system of equations. In the following exercises, determine if the following points are solutions to the given system of equations.

2x+y=5x+y=1

(a)(4,-3)

(b)(2,0)

In the following exercises, translate to a system of equations and solve.

The perimeter of a rectangle is 50. The length is 5 more than the width. Find the length and width.
See all solutions

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