Steps Systems of Equations by Substitution

What is the first step in solving a system by Substitution?

• Make sure both equations are in standard form.

• Make sure at least one equation is solved for one variable.

• Make sure both equations are in slope-intercept form.

Why does substitution help us solve a system of equations?

• It changes one variable to an expression using the other variable, so we can solve an equation that only has one variable at a time.

• It creates a problem with fewer steps.

• It puts both equations in slope-intercept form for easy graphing.

TRUE or FALSE:

When both equations have the same variable isolated

(both y = or both x = ),

substituting the first into the second ends up looking like

you just set the two equal to each other.

• TRUE

• FALSE

Which option shows the CORRECT substitution for this system?

Find the value of (x, y) that satisfies the equations by solving the system using substitution.
 
5x + 4y= −14
y =  −7x  −  15  The solution is (a)   .

• (-2, -1)

• (0, 0)

• (1, 1)

• (2, 2)

Solve the system of linear equations by substitution.

-5x + 3y = 51

y = 10x - 8​

​ ​ ​ (a)   ​ (b)  

• y = -22

• x = -3

• x = 59/25

• y = 15.6

• x = 3

• y = 22

• x = -8

• y = 4

Solve the system of linear equations by substitution.

• x = 6

• x = -3

• y = 2

• y = 5/9

• x = 1

• y = 1

• x = -8

• y = 4

• x = -2

Solve by Substitution:

x = -3y - 17

2x + 3y = -7

• (1, -20)

• (3, 0)

• (-5, -2)

• (10 , -9)

Solve the system of linear equations by substitution.

• y = -22

• x = -3

• x = 1

• y = -4

• x = 5

• y = -8

• x = -8

• y = 4

What is the first step when solving the system using the substitution method?

y=2x+4

2x+3y=20

Substitute ​ (a)   ​ for ​ (b)   in the 2nd equation to get ​ (c)  

• 2x+4

• y

• 2x+3(2x+4)=20

Answer explanation

y=2x+4

2x+3y=20

Substitute 2x+4 for y in 2x+3y=20 to get:

2x+3(2x+4)=20

then you can solve that equation for x