{y = 5x + 7 3y − 15x = 18
{x − 2y = 6 3x − 6y = 18
{y = 3x + 6 y = −13x − 4
{y = 2/3x − 1 y=2/3x − 2
Match the system of equations to the number of solutions it has.
Infinite Solutions
No Solutions
One Solution
{y = 5x + 7 3y − 15x = 18 - One Solution
{x − 2y = 6 3x − 6y = 18 - No Solutions
{y = 3x + 6 y = −13x − 4 - One Solution
{y = 2/3x − 1 y = 2/3x − 2 - Infinite Solutions
{y = 5x + 7 3y − 15x = 18
{x − 2y = 6 3x − 6y = 18
{y = 3x + 6 y = −1/3x − 4
{y = 2/3x − 1 y=2/3x − 2
Match the system of equations to the number of solutions it has.
Infinite Solutions
No Solutions
One Solution
{y = 5x + 7 3y − 15x = 18 - One Solution
{x − 2y = 6 3x − 6y = 18 - No Solutions
{y = 3x + 6 y = −1/3x − 4 - One Solution
{y = 2/3x − 1 y = 2/3x − 2 - Infinite Solutions
Put the steps in order that are used to solve the following systems of equations by substitution. {−7x − 2y = −13 x − 2y = 11
y = −4
−7(2y + 11) − 2y = −13
(3,−4)
−16y = 64
x − 2y = 11→ x = 2y + 11
−16y − 77 = −13
−14y − 77 − 2y = −13
x = 2(−4) + 11→ x = 3
1. x - 2y = 11 → x = 2y + 11
2. −7x - 2y = −13
3. Substitute x = 2y + 11 into the equation −7x - 2y = −13:
-7(2y + 11) - 2y = -13
4. Solve for y: -16y - 77 = -13
5. y = -4
6. Substitute y = -4 into x = 2y + 11:
x = 2(-4) + 11 → x = 3
7. The solution is (3, -4)
are you sure
I apologize for the mistake. Here are the steps in the correct order:
1. x - 2y = 11
2. −7x - 2y = −13
3. Substitute x = 2y + 11 into the equation −7x - 2y = −13:
-7(2y + 11) - 2y = -13
4. Solve for y: -14y - 77 - 2y = -13
5. Simplify to -16y = 64
6. Solve for y: y = -4
7. Substitute y = -4 into x = 2y + 11:
x = 2(-4) + 11 → x = 3
8. The solution is (3, -4)