Solving Systems by Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Tags

CCSS.7.EE.B.4A

Front

What is the first step in solving the system: y - 1 = 2x and y = 4x - 1?

Back

The first step is to solve one of the equations for y, which is already done in the second equation: y = 4x - 1.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system: y = -2x + 18 and y = 8?

Back

To find the solution, set -2x + 18 = 8, solve for x, and then substitute back to find y. The solution is (5, 8).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two lines intersect at a point?

Back

If two lines intersect at a point, it means that there is a unique solution to the system of equations represented by those lines.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the y-intercept in an equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you check if your solution to a system of equations is correct?

Back

You can check the solution by substituting the values of x and y back into both original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system: y + 8 = 3x and y = 4 - x?

Back

To find the solution, substitute y from the second equation into the first. The solution is (3, 1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6